गणित

1-If 2x-y=4 then 6x-3y=?
(a)15
(b)12
(c)18
(d)10
Ans. (b)
2-If x=y=2z and xyz=256 then what is the value of x?
(a)12
(b)8
(c)16
(d)6
Ans. (b)
3-(1/10)18 - (1/10)20 = ?
(a) 99/1020
(b) 99/10
(c) 0.9
(d) none of these
Ans. (a)
4-Pipe A can fill in 20 minutes and Pipe B in 30 mins and Pipe C can empty the same in 40 mins.If all of them work together, find the time taken to fill the tank
(a) 17 1/7 mins
(b) 20 mins
(c) 8 mins
(d) none of these
Ans. (a)
5-Thirty men take 20 days to complete a job working 9 hours a day. How many hour a day should 40 men work to complete the job?
(a) 8 hrs
(b) 7 1/2 hrs
(c) 7 hrs
(d) 9 hrs
Ans. (b)
6-Find the smallest number in a GP whose sum is 38 and product 1728
(a) 12
(b) 20
(c) 8
(d) none of these
Ans. (c)
7-A boat travels 20 kms upstream in 6 hrs and 18 kms downstream in 4 hrs. Find the speed of the boat in still water and the speed of the water current?
(a) 1/2 kmph
(b) 7/12 kmph
(c) 5 kmph
(d) none of these
Ans. (b)
8-A goat is tied to one corner of a square plot of side 12m by a rope 7m long. Find the area it can graze?
(a) 38.5 sq.m
(b) 155 sq.m
(c) 144 sq.m
(d) 19.25 sq.m

Ans. (a)
9-Mr. Shah decided to walk down the escalator of a tube station. He found that if he walks down 26 steps, he requires 30 seconds to reach the bottom. However, if he steps down 34 stairs he would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the height of the stair way in steps?
Ans.46 steps.
10-The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member ?
Ans.40 years.
11-ABCE is an isosceles trapezoid and ACDE is a rectangle. AB = 10 and EC = 20. What is the length of AE?
Ans. AE = 10.
12- In the given figure, PA and PB are tangents to the circle at A and B respectively and the chord BC is parallel to tangent PA. If AC = 6 cm, and length of the tangent AP is 9 cm, then what is the length of the chord BC?
Ans. BC = 4 cm.
13-Three cards are drawn at random from an ordinary pack of cards. Find the probability that they will consist of a king, a queen and an ace.
Ans. 64/2210.
14-A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice. Each cat killed more mice than there were cats. How many cats do you think there were ?
Ans. 991.
15-If Log2 x - 5 Log x + 6 = 0, then what would the value / values of x be?
Ans. x = e2 or e3.
16-The square of a two digit number is divided by half the number. After 36 is added to the quotient, this sum is then divided by 2. The digits of the resulting number are the same as those in the original number, but they are in reverse order. The ten's place of the original number is equal to twice the difference between its digits. What is the number?
Ans. 46
17-Can you tender a one rupee note in such a manner that there shall be total 50 coins but none of them would be 2 paise coins.?
Ans. 45 one paisa coins, 2 five paise coins, 2 ten paise coins, and 1 twenty-five paise coins.
18-A monkey starts climbing up a tree 20ft. tall. Each hour, it hops 3ft. and slips back 2ft. How much time would it take the monkey to reach the top?
Ans.18 hours.
19-What is the missing number in this series?
8 2 14 6 11 ? 14 6 18 12
Ans. 9
20-A certain type of mixture is prepared by mixing brand A at Rs.9 a kg. with brand B at Rs.4 a kg. If the mixture is worth Rs.7 a kg., how many kgs. of brand A are needed to make 40kgs. of the mixture?
Ans. Brand A needed is 24kgs.

21-A wizard named Nepo says "I am only three times my son's age. My father is 40 years more than twice my age. Together the three of us are a mere 1240 years old." How old is Nepo?
Ans. 360 years old.
22-One dog tells the other that there are two dogs in front of me. The other one also shouts that he too had two behind him. How many are they?
Ans. Three.
23-A man ate 100 bananas in five days, each day eating 6 more than the previous day. How many bananas did he eat on the first day?
Ans. Eight.
24-If it takes five minutes to boil one egg, how long will it take to boil four eggs?
Ans. Five minutes.
25-The minute hand of a clock overtakes the hour hand at intervals of 64 minutes of correct time. How much a day does the clock gain or lose?
Ans. 32 8/11 minutes.
26-Solve for x and y: 1/x - 1/y = 1/3, 1/x2 + 1/y2 = 5/9.
Ans. x = 3/2 or -3 and y = 3 or -3/2.
27-Daal is now being sold at Rs. 20 a kg. During last month its rate was Rs. 16 per kg. By how much percent should a family reduce its consumption so as to keep the expenditure fixed?
Ans. 20 %.
28-Find the least value of 3x + 4y if x2y3 = 6.
Ans. 10.
29-Can you find out what day of the week was January 12, 1979?
Ans. Friday.
30-A garrison of 3300 men has provisions for 32 days, when given at a rate of 850 grams per head. At the end of 7 days a reinforcement arrives and it was found that now the provisions will last 8 days less, when given at the rate of 825 grams per head. How, many more men can it feed?
Ans. 1700 men.
31-From 5 different green balls, four different blue balls and three different red balls, how many combinations of balls can be chosen taking at least one green and one blue ball?
Ans. 3720.
32-Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 15 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled?
Ans. 167 minutes.
33-A person walking 5/6 of his usual rate is 40 minutes late. What is his usual time?
Ans. 3 hours 20 minutes.


For a motorist there are three ways going from City A to City C. By way of bridge the distance is 20 miles and toll is $0.75. A tunnel between the two cities is a distance of 10 miles and toll is $1.00 for the vehicle and driver and $0.10 for each passenger. A two-lane highway without toll goes east for 30 miles to city B and then 20 miles in a northwest direction to City C.

1. Which is the shortest route from B to C
(a) Directly on toll free highway to City C
(b) The bridge
(c) The Tunnel
(d) The bridge or the tunnel
(e) The bridge only if traffic is heavy on the toll
free highway

Ans. (a)
2. The most economical way of going from City A to City B, in terms of toll and distance is to use the
(a) tunnel
(b) bridge
(c) bridge or tunnel
(d) toll free highway
(e) bridge and highway
Ans. (a)
3. Jim usually drives alone from City C to City A every working day. His firm deducts a percentage of employee pay for lateness. Which factor would most influence his choice of the bridge or the tunnel ?
(a) Whether his wife goes with him
(b) scenic beauty on the route
(c) Traffic conditions on the road, bridge and tunnel
(d) saving $0.25 in tolls
(e) price of gasoline consumed in covering additional
10 miles on the
bridge
Ans. (a)
4. In choosing between the use of the bridge and the tunnel the chief factor(s) would be:
I. Traffic and road conditions
II. Number of passengers in the car
III. Location of one's homes in the center or
outskirts of one of the
cities
IV. Desire to save $0.25

(a) I only
(b) II only
(c) II and III only
(d) III and IV only
(e) I and II only
Ans. (a)
The letters A, B, C, D, E, F and G, not necessarily in that order, stand for seven consecutive integers from 1 to 10
D is 3 less than A
B is the middle term
F is as much less than B as C is greater than D
G is greater than F

1. The fifth integer is
(a) A
(b) C
(c) D
(d) E
(e) F
Ans. (a)
2. A is as much greater than F as which integer is less than G
(a) A
(b) B
(c) C
(d) D
(e) E
Ans. (a)
3. If A = 7, the sum of E and G is
(a) 8
(b) 10
(c) 12
(d) 14
(e) 16
Ans. (a)
4. A - F = ?
(a) 1
(b) 2
(c) 3
(d) 4
(e) Cannot be determined
Ans. (a)
5. An integer T is as much greater than C as C isgreater than E. T can be written as A + E. What is D?
(a) 2
(b) 3
(c) 4
(d) 5
(e) Cannot be determined

Ans. (a)
6. The greatest possible value of C is how much greater than the smallest possible value of D?
(a) 2
(b) 3
(c) 4
(d) 5
(e) 6
Ans. (a)



In country X, democratic, conservative and justice parties have fought three civil wars in twenty years. TO restore stability an agreement is reached to rotate the top offices President, Prime Minister and Army Chief among the parties so that each party controls one and only one office at all times. The three top office holders must each have two deputies, one from each of the other parties. Each deputy must choose a staff composed of equally members of his or her chiefs party and member of the third party.

When Justice party holds one of the top offices, which of the following cannot be true
(a) Some of the staff members within that office are
justice party members
(b) Some of the staff members within that office are
democratic party
members
(c) Two of the deputies within the other offices are
justice party members
(d) Two of the deputies within the other offices are
conservative
party members
(e) Some of the staff members within the other offices
are justice
party members.
Ans. (a)
When the democratic party holds presidency, the staff of the prime minister's deputies are composed
I. One-fourth of democratic party members
II. One-half of justice party members and one-fourth
of conservative
party members
III. One-half of conservative party members and
one-fourth of justice
party members.

(a) I only
(b) I and II only
(c) II or III but not both
(d) I and II or I and III
(e) None of these
Ans. (a)
Which of the following is allowable under the rules as stated:
(a) More than half of the staff within a given office
belonging to a
single party
(b) Half of the staff within a given office belonging
to a single party
(c) Any person having a member of the same party as
his or her
immediate superior
(d) Half the total number of staff members in all
three offices
belonging to a single party
(e) Half the staff members in a given office belonging
to parties
different from the party of the top office holder in
that office.
Ans. (a)
The office of the Army Chief passes from Conservative to Justice party. Which of the following must be fired.
(a) The democratic deputy and all staff members
belonging to Justice party
(b) Justice party deputy and all his or hers staff
members
(c) Justice party deputy and half of his Conservative
staff members in
the chief of staff office
(d) The Conservative deputy and all of his or her
staff members
belonging to Conservative party
(e) No deputies and all staff members belonging to
conservative parties.
Ans. (a)
In recommendations to the board of trustees a tuition increase of $500 per year, the president of the university said "There were no student demonstrations over the previous increases of $300 last year and $200 the year before". If the president's statement is accurate then which of the following can be validly inferred from the information given:
I. Most students in previous years felt that the increases were justified because of increased operating costs.
II. Student apathy was responsible for the failure of students to protest the previous tuition increases.
III. Students are not likely to demonstrate over new tuition increases.

(a) I only
(b) II only
(c) I or II but not both
(d) I, II and III
(e) None
Ans. (a)


The office staff of XYZ corporation presently consists of three bookeepers--A, B, C and 5 secretaries D, E, F, G, H. The management is planning to open a new office in another city using 2 bookeepers and 3 secretaries of the present staff . To do so they plan to seperate certain individuals who don't function well together. The following guidelines were established to set up the new office
I. Bookeepers A and C are constantly finding fault
with one another
and should not be sent together to the new office as a
team
II. C and E function well alone but not as a team ,
they should be
seperated
III. D and G have not been on speaking terms and
shouldn't go together
IV Since D and F have been competing for promotion
they shouldn't be a
team

1-If A is to be moved as one of the bookeepers, which of the following cannot be a possible working unit.

A.ABDEH
B.ABDGH
C.ABEFH
D.ABEGH
Ans.B
2-If C and F are moved to the new office, how many combinations are possible
A.1
B.2
C.3
D.4
Ans.A
3-If C is sent to the new office,which member of the staff cannot go with C
A.B
B.D
C.F
D.G
Ans.B
4-Under the guidelines developed, which of the following must go to the new office
A.B
B.D
C.E
D.G
Ans.A
5-If D goes to the new office, which of the following is/are true
I.C cannot go
II.A cannot go
III.H must also go

A.I only
B.II only
C.I and II only
D.I and III only
Ans.D


After months of talent searching for an administrative assistant to the president of the college the field of applicants has been narrowed down to 5--A, B, C, D, E .It was announced that the finalist would be chosen after a series of all-day group personal interviews were held. The examining committee agreed upon the following procedure
I. The interviews will be held once a week
II. 3 candidates will appear at any all-day interview
session
III. Each candidate will appear at least once
IV. If it becomes necessary to call applicants for
additional interviews, no more 1 such applicant should be asked
to appear the
next week
V. Because of a detail in the written applications, it
was agreed that
whenever candidate B appears, A should also be
present.
VI. Because of travel difficulties it was agreed that C
will appear for
only 1 interview.
>

1-At the first interview the following candidates appear A,B,D. Which of the following combinations can be called for the interview to be held next week.
A.BCD
B.CDE
C.ABE
D.ABC
Ans.B
2-Which of the following is a possible sequence of combinations for interviews in 2 successive weeks
A.ABC;BDE
B.ABD;ABE
C.ADE;ABC
D.BDE;ACD
Ans.C
3-If A ,B and D appear for the interview and D is called for additional interview the following week, which 2 candidates may be asked to appear with D?
I. A
II B
III.C
IV.E
A.I and II
B.I and III only
C.II and III only
D.III and IV only
Ans.D
4-Which of the following correctly state(s) the procedure followed by the search committee
I.After the second interview all applicants have
appeared at least once
II.The committee sees each applicant a second time
III.If a third session,it is possible for all
applicants to appear at
least twice

A.I only
B.II only
C.III only
D.Both I and II
Ans.A


A certain city is served by subway lines A,B and C and numbers 1 2 and 3 When it snows , morning service on B is delayed When it rains or snows , service on A, 2 and 3 are delayed both in the morning and afternoon When temp. falls below 30 degrees Fahrenheit afternoon service is cancelled in either the A line or the 3 line,
but not both. When the temperature rises over 90 degrees Fahrenheit, the afternoon service is cancelled in either the line C or the 3 line but not both. When the service on the A line is delayed or cancelled, service on the C line which connects the A line, is delayed. When service on the 3 line is cancelled, service on the B line which connects the 3 line is delayed.

1-On Jan 10th, with the temperature at 15 degree Fahrenheit, it snows all day. On how many lines will service be affected, including both morning and afternoon.
(A) 2
(B) 3
(C) 4
(D) 5
Ans. D
2-On Aug 15th with the temperature at 97 degrees Fahrenheit it begins to rain at 1 PM. What is the minimum number of lines on which service will be affected?
(A) 2
(B) 3
(C) 4
(D) 5
Ans. C
3-On which of the following occasions would service be on the greatest number of lines disrupted.
(A) A snowy afternoon with the temperature at 45
degree farenheit
(B) A snowy morning with the temperature at 45 degree
farenheit
(C) A rainy afternoon with the temperature at 45
degree farenheit
(D) A rainy afternoon with the temperature at 95
degree farenheit
Ans. B



In a certain society, there are two marriage groups, red and brown. No marriage is permitted within a group. On marriage, males become part of their wives groups; women remain in their own group. Children belong to the same group as their parents. Widowers and divorced males revert to the group of their birth. Marriage to more than one person at the same time and marriage to a direct descendant are forbidden

Q1. A brown female could have had I. A grandfather born Red
II. A grandmother born Red
III Two grandfathers born Brown
(A) I only
(B) III only
(C) I, II and III
(D) I and II only
Ans. D
Q2. A male born into the brown group may have
(A) An uncle in either group
(B) A brown daughter
(C) A brown son
(D) A son-in-law born into red group
Ans. A
Q3. Which of the following is not permitted under the rules as stated.
(A) A brown male marrying his father's sister
(B) A red female marrying her mother's brother
(C) A widower marrying his wife's sister
(D) A widow marrying her divorced daughter's
ex-husband
Ans. B
Q4. If widowers and divorced males retained their group they had upon marrying which of the following would be permissible (Assume that no previous marriage occurred)
(A) A woman marrying her dead sister's husband
(B) A woman marrying her divorced daughter's
ex-husband
(C) A widower marrying his brother's daughter
(D) A woman marrying her mother's brother who is a
widower.

Ans. D


There are six steps that lead from the first to the second floor. No two people can be on the same step Mr. A is two steps below Mr. C Mr. B is a step next to Mr. D Only one step is vacant ( No one standing on that step )Denote the first step by step 1 and second step by step 2 etc.
1. If Mr. A is on the first step, Which of the following is true?
(a) Mr. B is on the second step
(b) Mr. C is on the fourth step.
(c) A person Mr. E, could be on the third step
(d) Mr. D is on higher step than Mr. C.
Ans: (d)
2. If Mr. E was on the third step & Mr. B was on a higher step than Mr. E which step must be vacant
(a) step 1
(b) step 2
(c) step 4
(d) step 5
(e) step 6
Ans: (a)
3. If Mr. B was on step 1, which step could A be on?
(a) 2&e only
(b) 3&5 only
(c) 3&4 only
(d) 4&5 only
(e) 2&4 only
Ans: (c)
4. If there were two steps between the step that A was standing and the step that B was standing on, and A was on a higher step than D , A must be on step
(a) 2
(b) 3
(c) 4
(d) 5
(e) 6
Ans: (c)
5. Which of the following is false
i. B&D can be both on odd-numbered steps in one
configuration
ii. In a particular configuration A and C must either
both an odd
numbered steps or both an even-numbered steps
iii. A person E can be on a step next to the vacant
step.
(a) i only
(b) ii only
(c) iii only
(d) both i and iii
Ans: (c)
Six swimmers A, B, C, D, E, F compete in a race. The outcome is as follows.
i. B does not win.
ii. Only two swimmers separate E & D
iii. A is behind D & E
iv. B is ahead of E , with one swimmer intervening
v. F is a head of D

1. Who stood fifth in the race ?
(a) A
(b) B
(c) C
(d) D
(e) E
Ans: (e)
2. How many swimmers separate A and F ?
(a) 1
(b) 2
(c) 3
(d) 4
(e) cannot be determined
Ans: (d)
3. The swimmer between C & E is
(a) none
(b) F
(c) D
(d) B
(e) A
Ans: (a)
4. If the end of the race, swimmer D is disqualified by the Judges then swimmer B finishes in which place
(a) 1
(b) 2
(c) 3
(d) 4
(e) 5
Ans: (b)


Five houses lettered A,B,C,D, & E are built in a row next to each other. The houses are lined up in the order A,B,C,D, & E. Each of the five houses has a colored chimney. The roof and chimney of each house must be painted as follows.
i. The roof must be painted either green, red ,or yellow.
ii. The chimney must be painted either white, black,
or red.
iii. No house may have the same color chimney as the
color of roof.
iv. No house may use any of the same colors that the
every next house
uses.
v. House E has a green roof.
vi. House B has a red roof and a black chimney

1. Which of the following is true ?
(a) At least two houses have black chimney.
(b) At least two houses have red roofs.
(c) At least two houses have white chimneys
(d) At least two houses have green roofs
(e) At least two houses have yellow roofs
Ans: (c)
2. Which must be false ?
(a) House A has a yellow roof
(b) House A & C have different color chimney
(c) House D has a black chimney
(d) House E has a white chimney
(e) House B&D have the same color roof.
Ans: (b)
3. If house C has a yellow roof. Which must be true.
(a) House E has a white chimney
(b) House E has a black chimney
(c) House E has a red chimney
(d) House D has a red chimney
(e) House C has a black chimney
Ans: (a)
4. Which possible combinations of roof & chimney can house
I. A red roof 7 a black chimney
II. A yellow roof & a red chimney
III. A yellow roof & a black chimney

(a) I only
(b) II only
(c) III only
(d) I & II only
(e) I&II&III
Ans: (e)
One of the following is my secret word: AIM DUE MOD OAT TIE. With the list in front of you, if I were to tell you any one of my secret word, then you would be able to tell me the number of vowels in my secret word. Which is my secret word?
Ans.TIE
One of Mr. Horton, his wife, their son, and Mr. Horton's mother is a doctor and another is a lawyer.
a)If the doctor is younger than the lawyer, then the doctor and the lawyer are not blood relatives.
b)If the doctor is a woman, then the doctor and the lawyer are blood relatives.
c)If the lawyer is a man, then the doctor is a man.
Whose occupation you know?
Ans.Mr. Horton:he is the doctor.
Mr. and Mrs. Aye and Mr. and Mrs. Bee competed in a chess tournament. Of the three games played:
a)In only the first game were the two players married to each other.
b)The men won two games and the women won one game.
c)The Ayes won more games than the Bees.
d)Anyone who lost game did not play the subsequent game.
Who did not lose a game?
Ans.Mrs.Bee did not lose a game.
Three piles of chips--pile I consists one chip, pile II consists of chips, and pile III consists of three chips--are to be used in game played by Anita and Brinda. The game requires:
a)That each player in turn take only one chip or all chips from just one pile.
b)That the player who has to take the last chip loses.
c)That Anita now have her turn.
From which pile should Anita draw in order to win?
Ans.Pile II
Of Abdul, Binoy, and Chandini:
a)Each member belongs to the Tee family whose members always tell the truth or to the El family whose members always lie.
b)Abdul says ''Either I belong or Binoy belongs to a different family from the other two."
Whose family do you name of?
Ans.Binoy's family--El.
In a class composed of x girls and y boys what part of the class is composed of girls
A.y/(x + y)
B.x/xy
C.x/(x + y)
D.y/xy
Ans.C
What is the maximum number of half-pint bottles of cream that can be filled with a 4-gallon can of cream(2 pt.=1 qt. and 4 qt.=1 gal)

A.16
B.24
C.30
D.64
Ans.D
f the operation,^ is defined by the equation x ^ y = 2x + y, what is the value of a in 2 ^ a = a ^ 3

A.0
B.1
C.-1
D.4
Ans.B
A coffee shop blends 2 kinds of coffee, putting in 2 parts of a 33p. a gm. grade to 1 part of a 24p. a gm. If the mixture is changed to 1 part of the 33p. a gm. to 2 parts of the less expensive grade, how much will the shop save in blending 100 gms.

A.Rs.90
B.Rs.1.00
C.Rs.3.00
D.Rs.8.00
Ans.C
There are 200 questions on a 3 hr examination.Among these questions are 50 mathematics problems.It is suggested that twice as much time be spent on each maths problem as for each other question.How many minutes should be spent on mathematics problems

A.36
B.72
C.60
D.100
Ans.B
In a group of 15,7 have studied Latin, 8 have studied Greek, and 3 have not studied either. How many of these studied both Latin and Greek

A.0
B.3
C.4
D.5
Ans.B
If 13 = 13w/(1-w) ,then (2w)2 =

A.1/4
B.1/2
C.1
D.2
Ans.C
If a and b are positive integers and (a-b)/3.5 = 4/7, then

(A) b < a
(B) b > a
(C) b = a
(D) b >= a
Ans. A
In june a baseball team that played 60 games had won 30% of its game played. After a phenomenal winning streak this team raised its average to 50% .How many games must the team have won in a row to attain this average?

A. 12
B. 20
C. 24
D. 30
Ans. C
M men agree to purchase a gift for Rs. D. If three men drop out how much more will each have to contribute towards the purchase of the gift/

A. D/(M-3)
B. MD/3
C. M/(D-3)
D. 3D/(M2-3M)
Ans. D
A company contracts to paint 3 houses. Mr.Brown can paint a house in 6 days while Mr.Black would take 8 days and Mr.Blue 12 days. After 8 days Mr.Brown goes on vacation and Mr. Black begins to work for a period of 6 days. How many days will it take Mr.Blue to complete the contract?

A. 7
B. 8
C. 11
D. 12
Ans.C
2 hours after a freight train leaves Delhi a passenger train leaves the same station travelling in the same direction at an average speed of 16 km/hr. After travelling 4 hrs the passenger train overtakes the freight train. The average speed of the freight train was?

A. 30
B. 40
C.58
D. 60
Ans. B
If 9x-3y=12 and 3x-5y=7 then 6x-2y = ?

A.-5
B. 4
C. 2
D. 8
Ans. D
There are 5 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe
Ans 5c1/ 9c1
What is the selling price of a car? If the cost of the car is Rs.60 and a profit of 10% over selling price is earned
Ans: Rs 66/-
1/3 of girls , 1/2 of boys go to canteen .What factor and total number of classmates go to canteen.
Ans: Cannot be determined.
The price of a product is reduced by 30% . By what percentage should it be increased to make it 100%
Ans: 42.857%
There is a square of side 6cm . A circle is inscribed inside the square. Find the ratio of the area of circle to square.
Ans. 11/14
There are two candles of equal lengths and of different thickness. The thicker one lasts of six hours. The thinner 2 hours less than the thicker one. Ramesh lights the two candles at the same time. When he went to bed he saw the thicker one is twice the length of the thinner one. How long ago did Ramesh light the two candles .
Ans: 3 hours.
If PQRST is a parallelogram what it the ratio of triangle PQS & parallelogram PQRST .
Ans: 1:2
The cost of an item is Rs 12.60. If the profit is 10% over selling price what is the selling price ?
Ans: Rs 13.86/-
There are 6 red shoes & 4 green shoes . If two of red shoes are drawn what is the probability of getting red shoes
Ans: 6c2/10c2
To 15 lts of water containing 20% alcohol, we add 5 lts of pure water. What is % alcohol.
Ans : 15%
A worker is paid Rs.20/- for a full days work. He works 1,1/3,2/3,1/8.3/4 days in a week. What is the total amount paid for that worker ?
Ans : 57.50
If the value of x lies between 0 & 1 which of the following is the largest?

(a) x
(b) x2
(c) -x
(d) 1/x
Ans : (d)
If the total distance of a journey is 120 km .If one goes by 60 kmph and comes back at 40kmph what is the average speed during the journey?
Ans: 48kmph
A school has 30% students from Maharashtra .Out of these 20% are Bombay students. Find the total percentage of Bombay?
Ans: 6%
An equilateral triangle of sides 3 inch each is given. How many equilateral triangles of side 1 inch can be formed from it?
Ans: 9
If A/B = 3/5,then 15A = ?
Ans : 9B
Each side of a rectangle is increased by 100% .By what percentage does the area increase?
Ans : 300%
Perimeter of the back wheel = 9 feet, front wheel = 7 feet on a certain distance, the front wheel gets 10 revolutions more than the back wheel .What is the distance?
Ans : 315 feet.
Perimeter of front wheel =30, back wheel = 20. If front wheel revolves 240 times. How many revolutions will the back wheel take?
Ans: 360 times
20% of a 6 litre solution and 60% of 4 litre solution are mixed. What percentage of the mixture of solution
Ans: 36%
City A's population is 68000, decreasing at a rate of 80 people per year. City B having population 42000 is increasing at a rate of 120 people per year. In how many years both the cities will have same population?
Ans: 130 years
Two cars are 15 kms apart. One is turning at a speed of 50kmph and the other at 40kmph . How much time will it take for the two cars to meet?
Ans: 3/2 hours
A person wants to buy 3 paise and 5 paise stamps costing exactly one rupee. If he buys which of the following number of stamps he won't able to buy 3 paise stamps.
Ans: 9
Which of the following fractions is less than 1/3

(a) 22/62
(b) 15/46
(c) 2/3
(d) 1
Ans: (b)
There are two circles, one circle is inscribed and another circle is circumscribed over a square. What is the ratio of area of inner to outer circle?
Ans: 1 : 2
Three types of tea the a,b,c costs Rs. 95/kg,100/kg and70/kg respectively.
How many kgs of each should be blended to produce 100 kg of mixture worth Rs.90/kg, given that the quntities of band c are equal

a)70,15,15
b)50,25,25
c)60,20,20
d)40,30,30
Ans. (b)
in a class, except 18 all are above 50 years.
15 are below 50 years of age. How many people are there

(a) 30
(b) 33
(c) 36
(d) none of these.
Ans. (d)
If a boat is moving in upstream with velocity of 14 km/hr and goes downstream with a velocity of 40 km/hr, then what is the speed of the stream ?

(a) 13 km/hr
(b) 26 km/hr
(c) 34 km/hr
(d) none of these
Ans. A
Find the value of ( 0.75 * 0.75 * 0.75 - 0.001 ) / ( 0.75 * 0.75 - 0.075 + 0.01)

(a) 0.845
(b) 1.908
(c) 2.312
(d) 0.001
Ans. A
A can have a piece of work done in 8 days, B can work three times faster than the A, C can work five times faster than A. How many days will they take to do the work together ?

(a) 3 days
(b) 8/9 days
(c) 4 days
(d) can't say
Ans. B
A car travels a certain distance taking 7 hrs in forward journey, during the return journey increased speed 12km/hr takes the times 5 hrs. What is the distance travelled

(a) 210 kms
(b) 30 kms
(c) 20 kms
(c) none of these
Ans. B
Find (7x + 4y ) / (x-2y) if x/2y = 3/2 ?

(a) 6
(b) 8
(c) 7
(d) data insufficient
Ans. C
If on an item a company gives 25% discount, they earn 25% profit. If they now give 10% discount then what is the profit percentage.

(a) 40%
(b) 55%
(c) 35%
(d) 30%
Ans. D
A certain number of men can finish a piece of work in 10 days. If however there were 10 men less it will take 10 days more for the work to be finished. How many men were there originally?

(a) 110 men
(b) 130 men
(c) 100 men
(d) none of these
Ans. A
In simple interest what sum amounts of Rs.1120/- in 4 years and Rs.1200/- in 5 years ?

(a) Rs. 500
(b) Rs. 600
(c) Rs. 800
(d) Rs. 900
Ans. C
If a sum of money compound annually amounts of thrice itself in 3 years. In how many years will it become 9 times itself.

(a) 6
(b) 8
(c) 10
(d) 12
Ans A
Two trains move in the same direction at 50 kmph and 32 kmph respectively. A man in the slower train observes the 15 seconds elapse before the faster train completely passes by him. What is the length of faster train ?

(a) 100m
(b) 75m
(c) 120m
(d) 50m
Ans B
How many mashes are there in 1 square meter of wire gauge if each mesh
is 8mm long and 5mm wide ?

(a) 2500
(b) 25000
(c) 250
(d) 250000
Ans B
x% of y is y% of ?
(a) x/y
(b) 2y
(c) x
(d) can't be determined
Ans. C
The price of sugar increases by 20%, by what % should a housewife reduce the consumption of sugar so that expenditure on sugar can be same as before ?
(a) 15%
(b) 16.66%
(c) 12%
(d) 9%
Ans B
A man spends half of his salary on household expenses, 1/4th for rent, 1/5th for travel expenses, the man deposits the rest in a bank. If his monthly deposits in the bank amount 50, what is his monthly salary ?
(a) Rs.500
(b) Rs.1500
(c) Rs.1000
(d) Rs. 900
Ans C
15 men take 21 days of 8 hrs. each to do a piece of work. How many days of 6 hrs. each would it take for 21 women if 3 women do as much work as 2 men?
(a) 30
(b) 20
(c) 19
(d) 29
Ans. A
A cylinder is 6 cms in diameter and 6 cms in height. If spheres of the same size are made from the material obtained, what is the diameter of each sphere?
(a) 5 cms
(b) 2 cms
(c) 3 cms
(d) 4 cms
Ans C
The difference b/w the compound interest payble half yearly and the simple interest on a certain sum lent out at 10% p.a for 1 year is Rs 25. What is the sum?
(a) Rs. 15000
(b) Rs. 12000
(c) Rs. 10000
(d) none of these
Ans C
What is the smallest number by which 2880 must be divided in order to make it into a perfect square ?

(a) 3
(b) 4
(c) 5
(d) 6
Ans. C
A father is 30 years older than his son however he will be only thrice as old as the son after 5 years what is father's present age ?

(a) 40 yrs
(b) 30 yrs
(c) 50 yrs
(d) none of these
Ans. A
If an item costs Rs.3 in '99 and Rs.203 in '00.What is the % increase in price?

(a) 200/3 %
(b) 200/6 %
(c) 100%
(d) none of these
Ans. A
5 men or 8 women do equal amount of work in a day. a job requires 3 men and 5 women to finish the job in 10 days how many woman are required to finish the job in 14 days.

a) 10
b) 7
c) 6
d) 12
Ans 7
A simple interest amount of rs 5000 for six month is rs 200. what is the anual rate of interest?

a) 10%
b) 6%
c) 8%
d) 9%
Ans 8%
In objective test a correct answer score 4 marks and on a wrong answer 2 marks are ---. a student score 480 marks from 150 question. how many answer were correct?

a) 120
b) 130
c) 110
d) 150
Ans130.
An article sold at amount of 50% the net sale price is rs 425 .what is the list price of the article?

a) 500
b) 488
c) 480
d) 510
Ans 500
A man leaves office daily at 7pm A driver with car comes from his home to pick him from office and bring back home One day he gets free at 5:30 and instead of waiting for driver he starts walking towards home. In the way he meets the car and returns home on car He reaches home 20 minutes earlier than usual. In how much time does the man reach home usually??
Ans. 1hr 20min
A works thrice as much as B. If A takes 60 days less than B to do a work then find the number of days it would take to complete the work if both work together?
Ans. 22½days
How many 1's are there in the binary form of 8*1024 + 3*64 + 3
Ans. 4
A boy has Rs 2. He wins or loses Re 1 at a time If he wins he gets Re 1 and if he loses the game he loses Re 1.
He can loose only 5 times. He is out of the game if he earns Rs 5.
Find the number of ways in which this is possible?
Ans. 16
If there are 1024*1280 pixels on a screen and each pixel can have around 16 million colors
Find the memory required for this?
Ans. 4MB
On a particular day A and B decide that they would either speak the truth or will lie.
C asks A whether he is speaking truth or lying?
He answers and B listens to what he said. C then asks B what A has said B says "A says that he is a liar"
What is B speaking ?

(a) Truth
(b) Lie
(c) Truth when A lies
(d) Cannot be determined
Ans. (b)
What is the angle between the two hands of a clock when time is 8:30
Ans. 75(approx)
A man walks east and turns right and then from there to his left and then 45degrees to his right. In which direction did he go
Ans. North west
A man shows his friend a woman sitting in a park and says that she the daughter of my grandmother's only son. What is the relation between the two
Ans. Daughter
If a=2/3b , b=2/3c, and c=2/3d what part of d is b/

(a) 8/27
(b) 4/9
(c) 2/3
(d) 75%
(e) 4/3
Ans. (b)
Successive discounts of 20% and 15% are equal to a single discount of

(a) 30%
(b) 32%
(c) 34%
(d) 35%
(e) 36
Ans. (b)
The petrol tank of an automobile can hold g liters. If a liters was removed when the tank was full, what part of the full tank was removed?

(a)g-a
(b)g/a
(c) a/g
(d) (g-a)/a
(e) (g-a)/g
Ans. (c)
If x/y=4 and y is not '0' what % of x is 2x-y

(a)150%
(b)175%
(c)200%
(d)250%
Ans. (b)
A three digit number consists of 9,5 and one more number . When these digits are reversed and then subtracted from the original number the answer yielded will be consisting of the same digits arranged yet in a different order. What is the other digit?

Sol. Let the digit unknown be n.
The given number is then 900+50+n=950+n.

When reversed the new number is 100n+50+9=59+100n.
Subtracting these two numbers we get 891-99n.
The digit can be arranged in 3 ways or 6 ways.
We have already investigated 2 of these ways.
We can now try one of the remaining 4 ways. One of these is n 95
100n+90+5=891-99n
or 199n =796
so, n=4
the unknown digit is 4.
A farmer built a fence around his 17 cows, in a square shaped region. He used 27 fence poles on each side of the square. How many poles did he need altogether???
Ans.104 poles

Sol. Here 25 poles Must be there on each side .And around four corners 4 poles will be present. 4*25+4=100+4=104 poles.
On the first test of the semester, kiran scored a 60. On the last test of the semester, kiran scored 75% By what percent did kiran's score improve?
Ans: 25%

Sol. In first test kiran got 60
In last test he got 75.
% increase in test ( 60(x+100))/100=75
0.6X+60=75
0.6X=15
X=15/0.6=25%
A group consists of equal number of men and women. Of them 10% of men and 45% of women are unemployed. If a person is randomly selected from the group. Find the probability for the selected person to be an employee.
Ans:29/40

Sol: Assume men=100,women=100 then employed men & women r (100-10)+(100-45)=145
So probability for the selected person to be an employee=145/200=29/40
Randy's chain of used car dealership sold 16,400 cars in 1998. If the chain sold 15,744 cars in 1999, by what percent did the number of cars sold decrease?
Ans: 4%

Sol. Let percentage of decrease is x , then
16400(100-x)/100=15744
16400-15744=164x
x=656/164=4%
A radio when sold at a certain price gives a gain of 20%. What will be the gain percent, if sold for thrice the price?
A) 260%
B) 150%
C) 100%
D) 50%
E) None of these
Ans: 260%

Sol. Let x be original cost of the radio.
The solding price = (100+20)x=120x
If , it is sold for thrice the price ,then 3*120x=360x
So, gain percent is (360-100)=260%.
If the Arithmetic mean is 34 and geometric mean is 16 then what is greates number in that series of numbers?
Ans. 64

Sol. Let two numbers be x, y;
Arthmetic mean=34=>( x+y)/2=34
x+y=68
geometric mean=16=>(xy)pow 1/2=16
xy=16*16=256
By trail and error 16*16=64*4
And 64+4/2=34
So the greatest number int hat series is 64.
The diameter of the driving wheel of a bus is 140cm. How many revolutions per minute must the wheel make in order to keep a speed of 66 kmph?
Ans. 250

Sol. Distance to be covered in 1 min=(66*1000)/60 m=1100m
Circumference of the wheel =(2*22/7*0.70)m=4.4m.
So, Number of revolutions per min=1100/4.4=250.
The boys and girls in a college are in the ratio 3:2. If 20% of the boys and 25% of the girls are adults, the percentage of students who are not adults is:??
Ans.78%

Sol: Suppose boys = 3x and girls = 2x
Not adults = (80*3x/100) + (75*2x/100) = 39x/10
Required percentage = (39x/10)*(1/5x)*100 = 78%
Vivek travelled 1200km by air which formed 2/5 of his trip. One third of the whole trip , he travelled by car and the rest of the journey he performed by train. The distance travelled by train was???
Ans.800km

Sol: Let the total trip be x km.
Then 2x/5=1200
x=1200*5/2=3000km
Distance travelled by car =1/3*3000=1000km
Journey by train =[3000-(1200+1000)]=800km.
In a college ,1/5 th of the girls and 1/8 th of the boys took part in a social camp. What of the total number of students in the college took part in the camp?
Ans: 2/13

Sol: Out of 5 girls 1 took part in the camp
out of 8 boys 1 took part in the camp
so, out of 13 students 2 took part in the camp.
So, 2/13of the total strength took part in the camp.
On sports day, if 30 children were made to stand in a column,16 columns could be formed. If 24 children were made to stand in a column , how many columns could be formed?
Ans. 20

Sol: Total number of children=30*16=480
Number of columns of 24 children each =480/24=20.
Two trains 200mts and 150mts are running on the parallel rails at this rate of 40km/hr and 45km/hr. In how much time will they cross each other if they are running in the same direction.
Ans: 252sec

Sol: Relative speed=45-40=5km/hr=25/18 mt/sec
Total distance covered =sum of lengths of trains =350mts.
So, time taken =350*18/25=252sec.
5/9 part of the population in a village are males. If 30% of the males are married, the percentage of unmarried females in the total population is:
Ans: (250/9)%

Sol: Let the population =x Males=(5/9)x
Married males = 30% of (5/9)x = x/6
Married females = x/6
Total females = (x-(5/9)x)=4x/9
Unmarried females = (4x/9 – x/6) = 5x/18
Required percentage = (5x/18 * 1/x * 100) = (250/9)%
From height of 8 mts a ball fell down and each time it bounces half the distance back. What will be the distance travelled
Ans.: 24

Sol. 8+4+4+2+2+1+1+0.5+0.5+ and etc .. =24
First day of 1999 is Sunday what day is the last day
Ans.: Monday
Increase area of a square by 69% by what percent should the side be increased
Ans.: 13

Sol:Area of square=x2
Then area of increase=100+69=169
square root of 169 i.e 13 .
Ten years ago, chandrawathi’s mother was four times older than her daughter. After 10years, the mother will be twice older than daughter. The present age of Chandrawathi is:
Ans.20 years

Sol: Let Chandrawathi’s age 10 years ago be x years.
Her mother’s age 10 years ago = 4x
(4x+10)+10=2(x+10+10)
x=10
Present age of Chandrawathi = (x+10) = 20years
Finding the wrong term in the given series
7, 28, 63, 124, 215, 342, 511
Ans:28

Sol: Clearly, the correct sequence is
2^3 – 1, 3^3 – 1, 4^3 – 1, 5^3 – 1, ……….
Therefore, 28 is wrong and should be replaced by (3^3 – 1) i.e, 26.
If a man walks at the rate of 5kmph, he misses a train by only 7min. However if he walks at the rate of 6 kmph he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station.
Ans:6km.

Sol: Let the required distance be x km.
Difference in the times taken at two speeds=12mins=1/5 hr.
Therefore x/5-x/6=1/5 or 6x-5x=6 or x=6km.
Hence ,the required distance is 6 km
Walking 5/6 of its usual speed, a train is 10min late. Find the usual time to cover the journey?
Ans:50 min

Sol: New speed = 5/6 of usual speed
New time = 6/5 of usual time
Therefore, (6/5 of usual time) – usual time = 10min
Therefore Usual time = 50min
A train running at 54 kmph takes 20 seconds to pass a platform. Next it takes 12 seconds to pass a man walking at 6 kmph in the same direction in which the train is going. Find the length of the train and the length of the platform.
Ans. length of the train=160m
length of the platform=140 m.

Sol: Let the length of the train be x meters and length of the platform be y meters.
Speed of the train relative to man=(54-6) kmph =48 kmph.
=(48*5/18) m/sec =40/3 m/sec.
In passing a man, the train covers its own length with relative speed.
Therefore, length of the train=(Relative speed *Time)
=(40/3 * 12) m =160 m.
Also, speed of the train=(54 * 5/18) m/sec=15 m/sec.
Therefore, x+y/2xy=20 or x+y=300 or y=(300-160 m=140 m.
Therefore, Length of the platform=140 m.
A man is standing on a railway bridge which is 180m long. He finds that a train crosses the bridge in 20seconds but himself in 8 seconds. Find the length of the train and its speed.
Ans: length of train=120m
Speed of train=54kmph

Sol: Let the length of the train be x meters
Then, the train covers x meters in 8 seconds and (x + 180) meters in 20 seconds.
Therefore x/8 = (x+180)/20 ó 20x = 8(x+180) ó x = 120
Therefore Length of the train = 120m
Speed of the train = 120/8 m/sec = 15 m/sec =15 * 18/5 kmph = 54kmph
A man sells an article at a profit of 25%. If he had bought it at 20 % less and sold it for Rs.10.50 less, he would have gained 30%. Find the cost price of the article?
Ans. Rs. 50.

Sol: Let the C.P be Rs.x.
1st S.P =125% of Rs.x.= 125*x/100= 5x/4.
2nd C.P=80% of x. = 80x/100 =4x/5.
2nd S.P =130% of 4x/5. = (130/100* 4x/5) = 26x/25.
Therefore, 5x/4-26x/25 = 10.50 or x = 10.50*100/21=50.
Hence, C.P = Rs. 50.
A grosser purchased 80 kg of rice at Rs.13.50 per kg and mixed it with 120 kg rice at Rs. 16 per kg. At what rate per kg should he sell the mixture to gain 16%?

Ans: Rs.17.40 per kg.
Sol: C.P of 200 kg of mix. = Rs (80*13.50+120*16) = Rs.3000.
S.P = 116% of Rs 3000= Rs (116*3000/100) = Rs.3480.
Rate of S.P of the mixture = Rs.3480/200.per kg. = Rs.17.40 per kg.
Two persons A and B working together can dig a trench in 8 hrs while A alone can dig it in 12 hrs. In how many hours B alone can dig such a trench?
Ans:24hours.

Sol: (A+B)’s one hour’s work =1/8, A’s one hour’s work =1/12
Therefore, B’s one hour’s work = (1/8-1/12) =1/24.
Hence, B alone can dig the trench in 24 hours.
A and B can do a piece of work in 12 days ; B and C can do it in 20 days. In how many days will A, B and C finishes it working all together?
Also, find the number of days taken by each to finish it working alone?
Ans:60 days

Sol: (A+B)’s one day’s work=1/12; (B+C)’s one day’s work=1/15 and (A+C)’s one day’s
work=1/20.
Adding, we get: 2(A+B+C)’s one day’s work = (1/12+1/15+1/20)=1/5.
Therefore, (A+B+C)’s one day’s work=1/10.
Thus, A, B and C together can finish the work in 10 days.
Now, A’s one day’s work
= [(A+B+C)’s one day’s work] – [(B+C)’s one day’s work]
= 1/10-1/15)
= 1/30.
Therefore, A alone can finish the work in 30 days.
Similarly, B’s 1 day’s work = (1/10 -1/20) = 1/20.
Therefore, B alone can finish the work in 20 days.
And, C’s 1 day’s work= (1/10-1/12) = 1/60.
Therefore, C alone can finish the work in 60 days.
A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work?
Ans:27 days.

Sol: (A’s 1 day’s work): (B’s 1 day’s work) = 2:1.
(A + B)’s 1 day’s work = 1/18.
Divide 1/18 in the ratio 2:1.
Therefore A’s 1 day’s work = (1/18 * 2/3) = 1/27.
Hence, A alone can finish the work in 27 days.
2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work?
Ans: 12 ½ days.

Sol: Let 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work =y.
Then, 2x+3y=1/10 and 3x+2y=1/8.
Solving, we get: x=7/200 and y=1/100.
Therefore (2 men +1 boy)’s 1 day’s work = (2*7/200 + 1*1/100) = 16/200 = 2/25.
So, 2 men and 1 boy together can finish the work in 25/2 =12 ½ days.
What was the day of the week on 12th January, 1979?
Ans: Friday

Sol: Number of odd days in (1600 + 300) years = (0 + 1) = 1 odd day.
78 years = (19 leap years + 59 ordinary years) = (38 + 59) odd days = 6 odd days
12 days of January have 5 odd days.
Therefore, total number of odd days= (1 + 6 + 5) = 5 odd days.
Therefore, the desired day was Friday.
Find the day of the week on 16th july, 1776.
Ans: Tuesday

Sol: 16th july, 1776 means = 1775 years + period from 1st january to 16th july
Now, 1600 years have 0 odd days.
100 years have 5 odd days.
75 years = 18 leap years + 57 ordinary years
= (36 + 57) odd days = 93 odd days
= 13 weeks + 2 odd days = 2 odd days
Therefore, 1775 years have (0 + 5 + 2) odd days = 0 odd days.
Now, days from 1st Jan to 16th july; 1776
Jan Feb March April May June July
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days
= (28 weeks + 2 days) odd days
Therefore, total number of odd days = 2
Therefore, the day of the week was Tuesday
Find the angle between the minute hand and hour hand of a click when the time is
7.20?
Ans: 100deg

Sol: Angle traced by the hour hand in 12 hours = 360 degrees.
Angle traced by it in 7 hrs 20 min i.e. 22/3 hrs = [(360/12) * (22/3)] = 220 deg.
Angle traced by minute hand in 60 min = 360 deg.
Angle traced by it in 20 min = [(360/20) * 60] = 120 deg.
Therefore, required angle = (220 - 120) = 100deg.
The minute hand of a clock overtakes the hours hand at intervals of 65 min of the correct time. How much of the day does the clock gain or lose?
Ans: the clock gains 10 10/43 minutes

Sol: In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes.
To be together again, the minute hand must gain 60 minutes over the hour hand.
55 minutes are gained in 60 min.
60 min. are gained in [(60/55) * 60] min == 65 5/11 min.
But they are together after 65 min.
Therefore, gain in 65 minutes = (65 5/11 - 65) = 5/11 min.
Gain in 24 hours = [(5/11) * (60*24)/65] = 10 10/43 min.
Therefore, the clock gains 10 10/43 minutes in 24 hours.
A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours. What will be the true time when the clock indicates 1 p.m. on the following day?
Ans. 48 min. past 12.

Sol: Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.
24 hours 10 min. of this clock = 24 hours of the correct clock.
145/6 hrs of this clock = 24 hours of the correct clock.
29 hours of this clock = [24 * (6/145) * 29] hrs of the correct clock
= 28 hrs 48 min of the correct clock.
Therefore, the correct time is 28 hrs 48 min. after 8 a.m.
This is 48 min. past 12.
At what time between 2 and 3 o’ clock will the hands 0a a clock together?
Ans: 10 10/11 min. past 2.

Sol: At 2 o’ clock, the hour hand is at 2 and the minute hand is at 12, i.e. they are 10 min space apart.
To be together, the minute hand must gain 10 minutes over the other hand.
Now, 55 minutes are gained by it in 60 min.
Therefore, 10 min will be gained in [(60/55) * 10] min = 10 10/11 min.
Therefore, the hands will coincide at 10 10/11 min. past 2.
A sum of money amounts to Rs.6690 after 3 years and to Rs.10035 after 6 years on compound interest. Find the sum.
Ans: Rs. 4460

Sol: Let the Sum be Rs. P. Then
P [1 + (R/100)]^3 = 6690………..(i)
P [1 + (R/100)]^6 = 10035………..(ii)
On dividing, we get [1 + (R/100)]^3 = 10035/6690 = 3/2.
P * (3/2) = 6690 or P = 4460.
Hence, the sum is Rs. 4460.
Simple interest on a certain sum is 16/25 of the sum. Find the rate percent and time, if both are numerically equal.
Ans: Rate = 8% and Time = 8 years

Sol: Let sum = X. Then S.I. = 16x/25
Let rate = R% and Time = R years.
Therefore, x * R * R/100 = 16x/25 or R^2 = 1600/25, R = 40/5 = 8
Therefore, Rate = 8% and Time = 8 years.
Find
i. S.I. on RS 68000 at 16 2/3% per annum for 9 months.
ii. S.I. on RS 6250 at 14% per annum for 146 days.
iii. S.I. on RS 3000 at 18% per annum for the period from 4th Feb 1995 to 18th April 1995.
Ans: i. RS 8500.
ii. RS 350.
iii. RS 108.

Sol:
i. P = 68000, R = 50/3% p.a. and T = 9/12 year = ¾ years
Therefore, S.I. = (P * Q * R/100)
= RS (68000 * 50/3 * ¾ * 1/100) = RS 8500.

ii. P = RS 6265, R = 14% p.a. and T = (146/365) year = 2/5 years.
Therefore, S.I. = RS (6265 * 14 * 2/5 *1/100) = RS 350.
iii. Time = (24 + 31 + 18) days = 73 days = 1/5 year

P = RS 3000 and R = 18% p.a.
Therefore, S.I. = RS (3000 * 18 * 1/5 * 1/100) = RS 108
A sum at simple interest at 13 ½% per annum amounts to RS 2502.50 after 4 years. Find the sum.
Ans: sum = RS 1625

Sol: Let sum be x. Then,
S.I. = (x * 27/2 * 4 * 1/100) = 27x/50
Therefore, amount = (x + 27x/50) = 77x/50
Therefore, 77x/50 = 2502.50 or x = 2502.50 * 50 / 77 = 1625
Hence, sum = RS 1625
A sum of money doubles itself at C.I. in 15 years. In how many years will it become eight times?
Ans.45 years.

Sol: P [1 + (R/100)]^15 = 2P è [1 + (R/100)]^15 = 2……….(i)
Let P [1 + (R/100)]^n = 8P è P [1 + (R/100)]^n = 8 = 2^3
= [{1 + (R/100)}^15]^3.
è [1 + (R/100)]^n = [1 + (R/100)]^45.
è n = 45.
Thus, the required time = 45 years.
A certain sum amounts to Rs. 7350 in 2 years and to Rs. 8575 in 3 years. Find the sum and rate percent.
Ans: Sum = Rs. 5400,Rate=16 2/3 %.

Sol: S.I. on Rs. 7350 for 1 year = Rs. (8575-7350) = Rs. 1225.
Therefore, Rate = (100*1225 / 7350*1) % = 16 2/3 %.
Let the sum be Rs. X. then, x[1 + (50/3*100)]^2 = 7350.
è x * 7/6 * 7/6 = 7350.
è x = [7350 * 36/49] = 5400.
Therefore, Sum = Rs. 5400.
A, B and C start a business each investing Rs. 20000. After 5 months A withdrew Rs. 5000, B withdrew Rs. 4000 and C invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69,900 was recorded. Find the share of each.
Ans. A’s share = Rs. 20,500
B’s share = Rs. 21200
C’s share = Rs. 28200

Sol: Ratio of the capitals of A, B and C
= (20000*5+ 15000*7) : (20000*5+16000*7): (20000*5+26000*7)
=205000: 212000 : 282000 = 205:212:282
Therefore, A’s share = Rs. ( 69900*205/699) = Rs. 20,500
B’s share = Rs. (69900*212/699) = Rs. 21200,
C’s share = Rs. (69900*282/699) = Rs. 28200.
Sanjiv started a business by investing Rs. 36000. After 3 months Rajiv joined him by investing Rs. 36000. Out an annual profit of Rs. 37100, find the share of each?

Sol: Ratio of their capitals= 36000*12:36000*9 = 4:3
Sanjiv’s share= Rs. ( 37100*4/7) = Rs. 21200.
Rajiv’s share = Rs. ( 37100*3/7) = Rs.15900.
If 20 men can build a wall 56m long in 6 days, what length of a similar wall can be built by 35 men in 3 days?
Ans. Length=49m.

Sol: Since the length is to be found out, we compare each item with the length as shown below.
More men, more length built (Direct).
Less days, less length built (Direct).
Men 20:35 :: 56: x
Similarly, days 6:3 :: 56: x.
Therefore, 20*6*x= 35*3*56 or x= 49.
Hence, the required length= 49m.
If 9 engines consume 24 metric tonnes of coal, when each is working 8 hours a day; how much coal will be required for 8 engines, each running 13 hours a day, it being given that 3 engines of the former type consume as much as 4 engines of latter type.
Ans:26metric tonnes.

Sol: We shall compare each item with the quantity of coal.
Less engines, less coal consumed (direct)
More working hours, more coal consumed (direct)
If 3 engines of former type consume 1 unit, then 1 engine will consume 1/3 unit.
If 4 engines of latter type consume 1 unit, then 1 engine will consume 1/4 unit.
Less rate of consumption, less coal consumed (direct).
Therefore, number of engines 9:8 :: 24:x
Working hours 8:13 :: 24:x
Rate of consumption 1/3:1/4 :: 24:x.
9*8*1/3*x= 8*13*1/4*24 or x= 26.
Therefore, required consumption of coal 26 metric tonnes.
A contract is to be completed in 46 days and 117 men were set to work, each working 8 hours a day. After 33 days 4/7 of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day?
Ans.81

Sol: Remaining work = 1-4/7 =3/7.
Remaining period = (46-33) days =13 days.
Less work, less men (direct)
Less days, more men (indirect).
More hours per day, less men (indirect)
Therefore, work 4/7:3/7 ::117/x
Days 13:33 :: 117/x
Hrs/day 9:8:: 117/x
Therefore, 4/7*13*9*x= 3/7*33*8*117 or x= 198.
Therefore, additional men to be employed =(198-117) =81.
A garrison of 3300 men had provisions for 32 days, when given at the rate of 850gms per head. At the end of 7 days, reinforcement arrives and it was found that the provisions will last 17 days more, when given at the rate of 825gms per head. What is the strength of the reinforcement?
Ans: 1700

Sol: The problem becomes:
3300 men taking 850gms per head have provisions for (32-7) or 25 days. How many
men taking 825gms each have provisions for 17 days?
Less ration per head, more men (indirect).
Less days, more men (indirect)
Ration 825:850::3300:x
Days 17:25::3300:x
Therefore, 825*17*x= 850*25*3300 or x= 5000.
Therefore, strength of reinforcement = 5000-3300 = 1700.
Find the slant height, volume, curved surface area and the whole surface area of a cone of radius 21 cm and height 28 cm.

Sol: Slant Height, l = √(r^2 + h^2) =√(21^2 + 28^2) = √1225 = 35 cm
Volume = 1/3пr^2h = (1/3 * 22/7 * 21 * 21 * 28) cm^3 = 12936 cm^3
Curved surface area = пrl = 22/7 * 21 *35 cm^3 = 2310 cm^2
Total Surface Area = (пrl + пr^2) = (2310 + 22/7 * 21 * 21) cm^2 = 3696 cm^2
If the radius of the sphere is increased by 50%, find the increase percent in volume and the increase percent in the surface area.

Sol: Let the original radius = R. Then, new radius = 150/100 R = 3R/2
Original Volume = 4/3пR^3, New volume = 4/3п(3 R/2)^3 = 9пR^3/2
Original surface area = 4пR^2 , New surface area = 4п(3R/2)^2 = 9пR^2
Increase % in surface area = (5пR^2/4пR^2 * 100)% = 125%
If each edge of a cube is increased by 50%, find the percentage increase in its surface area.

Sol: Let the original length of each edge = a
Then, Original surface area = 6a^2
New surface area = 6 * (3a/2)^2 = 27a^2/2
Increase percent in surface area = (15/2a^2 * 1/(6a^2) * 100)% = 125%
Find the number of the bricks, each measuring 25 cm by 12.5 cm by 7.5 cm, required to build a wall 6 m long, 5 m high and 50cm thick, while the mortar occupies 5% of the volume of the wall.

Sol: Volume of the Wall = (600 * 500 * 50) cu. Cm.
Volume of the bricks = 95% of the volume of the wall.
= (95/100 * 600 * 500 * 50) cu. Cm.
Volume of 1 brick = (25 * 25/2 * 75/2) cu. Cm.
Therefore, Number of bricks = (95/100 * (600 * 500 * 50 * 2 * 10)/(25 * 25 * 75))=6080
The base of a triangular field is three times its altitude. If the cost of cultivating the field at Rs. 24.68 per hectare be Rs. 333.18, find its base and height.

Sol: Area of the field = Total cost/Rate = (333.18/24.68) hectares =13.5 hectares.
= (13.5*10000) m^2 =135000m^2.
Let altitude = x meters and base = 3x meters.
Then, ½ *3x* x= 135000 or x^2 = 9000 or x= 300.
Therefore, base =900 m & altitude = 300m.
Find the area of a rhombus one side of which measures 20cm and one diagonal
24cm.

Sol: Let, other diagonal = 2x cm,
Since halves of diagonals and one side of rhombus form a right angled triangle
with side as hypotenuse, we have:
(20)^2 =(12)^2+x^2 or x=Ö(20)^2-(12)^2 =Ö256=16 cm.
Therefore, other diagonal = 32 cm.
X alone can do a piece of work in 15 days and Y alone can do it in 10 days. X and Y undertook to do it for Rs. 720. With the help of Z they finished it in 5 days. How much is paid to Z?

Sol. In one day X can finish 1/15th of the work.
In one day Y can finish 1/10th of the work.
Let us say that in one day Z can finish 1/Zth of the work.
When all the three work together in one day they can finish 1/15 + 1/10 + 1/Z = 1/5th of the work.
Therefore, 1/Z = 1/30.
Ratio of their efficiencies = 1/15: 1/10: 1/30 = 2: 3: 1.Therefore Z receives 1/6th of the total money.
According to their efficiencies money is divided as 240: 360: 120.
Hence, the share of Z = Rs. 120.
How many number of times will the digit ‘7' be written when listing the integers from 1 to 1000?

Sol:7 does not occur in 1000. So we have to count the number of times it appears between 1 and 999. Any number between 1 and 999 can be expressed in the form of xyz where 0 < x, y, z < 9.

1. The numbers in which 7 occurs only once. e.g 7, 17, 78, 217, 743 etc
This means that 7 is one of the digits and the remaining two digits will be any of the other 9 digits (i.e 0 to 9 with the exception of 7)

You have 1*9*9 = 81 such numbers. However, 7 could appear as the first or the second or the third digit. Therefore, there will be 3*81 = 243 numbers (1-digit, 2-digits and 3- digits) in which 7 will appear only once.

In each of these numbers, 7 is written once. Therefore, 243 times.

2. The numbers in which 7 will appear twice. e.g 772 or 377 or 747 or 77
In these numbers, one of the digits is not 7 and it can be any of the 9 digits ( 0 to 9 with the exception of 7). There will be 9 such numbers. However, this digit which is not 7 can appear in the first or second or the third place. So there are 3 * 9 = 27 such numbers.
In each of these 27 numbers, the digit 7 is written twice. Therefore, 7 is written 54 times.

3. The number in which 7 appears thrice - 777 - 1 number. 7 is written thrice in it.
Therefore, the total number of times the digit 7 is written between 1 and 999 is 243 + 54 + 3 = 300
P can give Q a start of 20 seconds in a kilometer race. P can give R a start of 200 meters in the same kilometer race. And Q can give R a start of 20 seconds in the same kilometer race. How long does P take to run the kilometer?

Solution:
P can give Q a start of 20 seconds in a kilometer race. So, if Q takes 'x' seconds to run a kilometer, then P will take x – 20 seconds to run the kilometer.

Q can give R a start of 20 seconds in a kilometer race. So, if R takes 'y' seconds to run a kilometer, then Q will take y – 20 seconds to run the kilometer.

We know Q takes x seconds to run a kilometer
Therefore, x = y – 20

Therefore, P will take x – 20 = y – 20 – 20 = y – 40 seconds to run a kilometer.

i.e. P can give R a start of 40 seconds in a kilometer race, as R takes y seconds to run a kilometer and P takes only y – 40 seconds to run the kilometer.

We also know that P can give R a start 200 meters in a km race.
This essentially means that R runs 200 meters in 40 seconds.
Therefore, R will take 200 seconds to run a km.

If R takes 200 seconds to run a km, then P will take 200 – 40 = 160 seconds to run a km.
A and B enter in to a partnership and A invests Rs. 10,000 in the partnership. At the end of 4 months he withdraws Rs.2000. At the end of another 5 months, he withdraws another Rs.3000. If B receives Rs.9600 as his share of the total profit of Rs.19,100 for the year, how much did B invest in the company?

Solution:
The total profit for the year is 19100. Of this B gets Rs.9600. Therefore, A would
get (19100 – 9600) = Rs.9500.
The partners split their profits in the ratio of their investments.

Therefore, the ratio of the investments of A : B = 9500 : 9600 = 95 : 96.

A invested Rs.10000 initially for a period of 4 months. Then, he withdrew Rs.2000.
Hence, his investment has reduced to Rs.8000 (for the next 5 months).
Then he withdraws another Rs.3000. Hence, his investment will stand reduced to Rs.5000 during the last three months.

So, the amount of money that he had invested in the company on a money-month basis
will be = 4 * 10000 + 5 * 8000 + 3 * 5000 = 40000 + 40000 + 15000 = 95000
If A had 95000 money months invested in the company, B would have had 96,000
money months invested in the company (as the ratio of their investments is 95 : 96).

If B had 96,000 money-months invested in the company, he has essentially invested
96000/12 = Rs.8000
A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture?

Solution:
The 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture.

Step 1. When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water.

Step 2. When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step.

Therefore, the ratio of milk and water is 18 : 2 or 9 : 1.
A zookeeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of the animals he found it to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo?

Solution:
Let the number of horses = x
Then the number of pigeons = 80 – x.
Each pigeon has 2 legs and each horse has 4 legs.
Therefore, total number of legs = 4x + 2(80-x) = 260
=>4x + 160 – 2x = 260
=>2x = 100
=>x = 50.
A group of workers can do a piece of work in 24 days. However as 7 of them were absent it took 30 days to complete the work. How many people actually worked on the job to complete it?

Solution:
Let the original number of workers in the group be 'x'
Therefore, actual number of workers = x-7.
We know that the number of manhours required to do the job is the same in both the cases.
Therefore, x (24) = (x-7).30
24x = 30x - 210
6x = 210
x = 35.
Therfore, the actual number of workers who worked to complete the job = x - 7 = 35 -7 = 28.
The ratio of marks obtained by vinod and Basu is 6:5. If the combined average of their percentage is 68.75 and their sum of the marks is 275, find the total marks for which exam was conducted.

Solution:
Let Vinod marks be 6x and Basu's is 5x. Therefore, the sum of the marks = 6x + 5x = 11x.
But the sum of the marks is given as 275 = 11x. We get x = 25 therefore, vinod marks is 6x = 150 and Basu marks = 5x = 125.
Therefore, the combined average of their marks = (150 + 125) / 2 = 137.5.
If the total mark of the exam is 100 then their combined average of their percentage is 68.75
Therefore, if their combined average of their percentage is 137.5 then the total marks would be (137.5 / 68.75)*100 = 200.
If the cost price of 20 articles is equal to the selling price of 16 articles, What is the percentage of profit or loss that the merchant makes?

Solution:
Let Cost price of 1 article be Re.1.
Therefore, Cost price of 20 articles = Rs. 20.
Selling price of 16 articles = Rs. 20
Therefore, Selling price of 20 articles = (20/16) * 20 = 25
Profit = Selling price - Cost price
= 25 - 20 = 5
Percentage of profit = Profit / Cost price * 100.
= 5 / 20 * 100 = 25% Profit
A candidate who gets 20% marks fails by 10 marks but another candidate who gets 42% marks gets 12% more than the passing marks. Find the maximum marks.

Solution:
Let the maximum marks be x.
From the given statement pass percentage is 42% - 12% = 30%
By hypothesis, 30% of x – 20% of x = 10 (marks)
i.e., 10% of x = 10
Therefore, x = 100 marks.
When processing flower-nectar into honeybees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 15% water?

Solution:
Flower-nectar contains 50% of non-water part.
In honey this non-water part constitutes 85% (100-15).
Therefore 0.5 X Amount of flower-nectar = 0.85 X Amount of honey = 0.85 X 1 kg
Therefore amount of flower-nectar needed = (0.85/0.5) * 1kg = 1.7 kg.
A man can row 50 km upstream and 72 km downstream in 9 hours. He can also row 70 km upstream and 90 km downstream in 12 hours. Find the rate of current.

Solution:
Let x and y be the upstream and downstream speed respectively.
Hence 50/x + 72/y = 9 and 70/x + 90/y = 12
Solving for x and y we get x = 10 km/hr and y = 18 km/hr
We know that Speed of the stream = 1/2 * (downstream speed - upstream speed) = 1/2 (18 – 10) = 4 km/hr.
How long will it take for a sum of money to grow from Rs.1250 to Rs.10,000, if it is invested at 12.5% p.a simple interest?

Solution:
Simple interest is given by the formula SI = (pnr/100), where p is the principal, n is the number of years for which it is invested, r is the rate of interest per annum
In this case, Rs. 1250 has become Rs.10,000.
Therefore, the interest earned = 10,000 – 1250 = 8750.
8750 = [(1250*n*12.5)/100]
=> n = 700 / 12.5 = 56 years.
The time in a clock is 20 minute past 2. Find the angle between the hands of the clock.

Solution:
Time is 2:20. Position of the hands: Hour hand at 2 (nearly).
Minute hand at 4
Angle between 2 and 4 is 60 degrees [(360/12) * (4-2)]
Angle made by the hour hand in 20 minutes is 10 degrees, since it turns through ½ degrees in a minute.
Therefore, angle between the hands is 60 degrees - 10 degrees = 50 degrees
A man buys an article for Rs. 27.50 and sells it for Rs. 28.60. Find his gain percent.

Solution:
C.P. = Rs.27.50, S.P. = Rs. 28.60.
Therefore Gain = Rs. (28.60 – 27.50) = Rs.1.10.
Therefore Gain % = (1.10*100/27.50) % = 4%.
Find S.P., when:
(i) C.P. = Rs. 56.25, gain = 20%.
(ii) C.P. = Rs. 80.40, loss = 15%.
Solution:

(i) S.P. = 120% of Rs. 56.25 = Rs. (120*56.25/100) = Rs. 67.50.
(ii) S.P. = 85% of Rs. 80.40 = Rs. (85*80.40/100) = Rs. 68.34.
A scooterist covers a certain distance at 36 kmph. How many meters does he cover in 2min?
Solution:
Speed = 36 kmph = 36 * 5/18 = 10mps
Therefore, Distance covered in 2 min = (10 * 2 * 60)m = 1200m
How often between 11 O'clock and 12 O'clock are the hands of the clock together at an integral number value?
Solution:
At 11 O'clock, the hour hand is 5 spaces apart from the minute hand.
During the next 60 minutes, i.e. between 11' O clock and 12' O clock the hour hand will move five spaces [integral values as denoted by the 56 minute, 57 minute, 58 minute, 59 minute and 60 minute positions].
For each of these 5 positions, the minute hand will be at the 12th minute, 24th minute, 36th minute, 48th minute and 60th minute positions.
Hence the difference between the positions of the hour hand and the minute hand will have an integral number of minutes between them.

i.e. 5 positions.
Given that on 27th February 2003 is Thursday. What was the day on 27th February 1603?
Solution:
After every 400 years, the same day occurs.
Thus, if 27th February 2003 is Thursday, before 400 years i.e., on 27th February 1603 has to be Thursday.
It was calculated that 75 men could complete a piece of work in 20 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?
Answer: 30 days.

Explanation:
Before:
One day work = 1 / 20
One man’s one day work = 1 / ( 20 * 75)
Now:
No. Of workers = 50
One day work = 50 * 1 / ( 20 * 75)

The total no. of days required to complete the work = (75 * 20) / 50 = 30
A student divided a number by 2/3 when he required to multiply by 3/2. Calculate the percentage of error in his result.
Answer:0 %

Explanation:
Since 3x / 2 = x / (2 / 3)
A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 950gm. for a kg. His gain is …%.
Answer: 5.3 %

Explanation:
He sells 950 grams of pulses and gains 50 grams.
If he sells 100 grams of pulses then he will gain (50 / 950) *100 = 5.26
A software engineer has the capability of thinking 100 lines of code in five minutes and can type 100 lines of code in 10 minutes. He takes a break for five minutes after every ten minutes. How many lines of codes will he complete typing after an hour?
Answer: 250 lines of codes
A man was engaged on a job for 30 days on the condition that he would get a wage of Rs. 10 for the day he works, but he have to pay a fine of Rs. 2 for each day of his absence. If he gets Rs. 216 at the end, he was absent for work for ... days.
Answer: 7 days

Explanation:
The equation portraying the given problem is:
10 * x – 2 * (30 – x) = 216 where x is the number of working days.
Solving this we get x = 23
Number of days he was absent was 7 (30-23) days.
A contractor agreeing to finish a work in 150 days, employed 75 men each working 8 hours daily. After 90 days, only 2/7 of the work was completed. Increasing the number of men by________ each working now for 10 hours daily, the work can be completed in time.
Answer: 150 men.

Explanation:
One day’s work = 2 / (7 * 90)
One hour’s work = 2 / (7 * 90 * 8)
One man’s work = 2 / (7 * 90 * 8 * 75)


The remaining work (5/7) has to be completed within 60 days, because the total number of days allotted for the project is 150 days.

So we get the equation

(2 * 10 * x * 60) / (7 * 90 * 8 * 75) = 5/7 where x is the number of men working after the 90th day.

We get x = 225

Since we have 75 men already, it is enough to add only 150 men.
what is a percent of b divided by b percent of a?
(a) a (b) b (c) 1 (d) 10 (e) 100
Answer: (c) 1

Explanation:
a percent of b : (a/100) * b
b percent of a : (b/100) * a

a percent of b divided by b percent of a : ((a / 100 )*b) / (b/100) * a )) = 1
A man bought a horse and a cart. If he sold the horse at 10 % loss and the cart at 20 % gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. The amount paid by him was Rs._______ for the horse and Rs.________ for the cart.
Answer:
Cost price of horse = Rs. 400 & the cost price of cart = 200.

Explanation:-
Let x be the cost price of the horse and y be the cost price of the cart.
In the first sale there is no loss or profit. (i.e.) The loss obtained is equal to the gain.

Therefore (10/100) * x = (20/100) * y

X = 2 * y -----------------(1)

In the second sale, he lost Rs. 10. (i.e.) The loss is greater than the profit by Rs. 10.

Therefore (5 / 100) * x = (5 / 100) * y + 10 -------(2)

Substituting (1) in (2) we get

(10 / 100) * y = (5 / 100) * y + 10

(5 / 100) * y = 10

y = 200

From (1) 2 * 200 = x = 400
A tennis marker is trying to put together a team of four players for a tennis tournament out of seven available. males - a, b and c; females – m, n, o and p. All players are of equal ability and there must be at least two males in the team. For a team of four, all players must be able to play with each other under the following restrictions:
b should not play with m,
c should not play with p, and
a should not play with o.

Which of the following statements must be false?
1. b and p cannot be selected together
2. c and o cannot be selected together
3. c and n cannot be selected together.
Answer:
3.

Explanation:
Since inclusion of any male player will reject a female from the team. Since there should be four member in the team and only three males are available, the girl, n should included in the team always irrespective of others selection.
Five farmers have 7, 9, 11, 13 & 14 apple trees, respectively in their orchards. Last year, each of them discovered that every tree in their own orchard bore exactly the same number of apples. Further, if the third farmer gives one apple to the first, and the fifth gives three to each of the second and the fourth, they would all have exactly the same number of apples. What were the yields per tree in the orchards of the third and fourth farmers?
Answer:
11 & 9 apples per tree.

Explanation:
Let a, b, c, d & e be the total number of apples bored per year in A, B, C, D & E ‘s orchard. Given that a + 1 = b + 3 = c – 1 = d + 3 = e – 6

But the question is to find the number of apples bored per tree in C and D ‘s orchard. If is enough to consider c – 1 = d + 3.

Since the number of trees in C’s orchard is 11 and that of D’s orchard is 13. Let x and y be the number of apples bored per tree in C & d ‘s orchard respectively.

Therefore 11 x – 1 = 13 y + 3

By trial and error method, we get the value for x and y as 11 and 9
Five boys were climbing a hill. J was following H. R was just ahead of G. K was between G & H. They were climbing up in a column. Who was the second?
Answer:
G.

Explanation:
The order in which they are climbing is R – G – K – H – J
John is undecided which of the four novels to buy. He is considering a spy thriller, a Murder mystery, a Gothic romance and a science fiction novel. The books are written by Rothko, Gorky, Burchfield and Hopper, not necessary in that order, and published by Heron, Piegon, Blueja and sparrow, not necessary in that order.

(1) The book by Rothko is published by Sparrow.
(2) The Spy thriller is published by Heron.
(3) The science fiction novel is by Burchfield and is not published by Blueja.
(4)The Gothic romance is by Hopper.

Pigeon publishes ____________.

The novel by Gorky ________________.

John purchases books by the authors whose names come first and third in alphabetical order. He does not buy the books ______.

On the basis of the first paragraph and statement (2), (3) and (4) only, it is possible to deduce that
1. Rothko wrote the murder mystery or the spy thriller
2. Sparrow published the murder mystery or the spy thriller
3. The book by Burchfield is published by Sparrow.
Answer:
Novel Name Author Publisher

Spy thriller Rathko Heron

Murder mystery Gorky Piegon

Gothic romance Burchfield Blueja

Science fiction Hopper Sparrow



Explanation:

Since Blueja doesn’t publish the novel by Burchfield and Heron publishes the novel spy thriller, Piegon publishes the novel by Burchfield.

Since Hopper writes Gothic romance and Heron publishes the novel spy thriller, Blueja publishes the novel by Hopper.

Since Heron publishes the novel spy thriller and Heron publishes the novel by Gorky, Gorky writes Spy thriller and Rathko writes Murder mystery.
If a light flashes every 6 seconds, how many times will it flash in ¾ of an hour?
Answer: 451 times.

Explanation:
There are 60 minutes in an hour.
In ¾ of an hour there are (60 * ¾) minutes = 45 minutes.
In ¾ of an hour there are (60 * 45) seconds = 2700 seconds.
Light flashed for every 6 seconds.
In 2700 seconds 2700/6 = 450 times.
The count start after the first flash, the light will flashes 451 times in ¾ of an hour.
If point P is on line segment AB, then which of the following is always true?
(1) AP = PB (2) AP > PB (3) PB > AP (4) AB > AP (5) AB > AP + PB
Answer:
(4)

Explanation:
Since p is a point on the line segment AB, AB > AP
All men are vertebrates. Some mammals are vertebrates. Which of the following conclusions drawn from the above statement is correct.

All men are mammals
All mammals are men
Some vertebrates are mammals.
None
Answer: (c)
Which of the following statements drawn from the given statements are correct?

Given:
All watches sold in that shop are of high standard. Some of the HMT watches are sold in that shop.
a) All watches of high standard were manufactured by HMT.
b) Some of the HMT watches are of high standard.
c) None of the HMT watches is of high standard.
d) Some of the HMT watches of high standard are sold in that shop.
Answer: (b) & (d)
If every alternative letter starting from B of the English alphabet is written in small letter, rest all are written in capital letters, how the month “ September” be written.

(1) SeptEMbEr (2) SEpTeMBEr (3) SeptembeR
(4) SepteMber (5) None of the above.
Answer:
(5).

Explanation:
Since every alternative letter starting from B of the English alphabet is written in small letter, the letters written in small letter are b, d, f...

In the first two answers the letter E is written in both small & capital letters, so they are not the correct answers. But in third and fourth answers the letter is written in small letter instead capital letter, so they are not the answers.
The length of the side of a square is represented by x+2. The length of the side of an equilateral triangle is 2x. If the square and the equilateral triangle have equal perimeter, then the value of x is _______.
Answer:
x = 4

Explanation:
Since the side of the square is x + 2, its perimeter = 4 (x + 2) = 4x + 8
Since the side of the equilateral triangle is 2x, its perimeter = 3 * 2x = 6x
Also, the perimeters of both are equal.
(i.e.) 4x + 8 = 6x
(i.e.) 2x = 8 è x = 4.
It takes Mr. Karthik y hours to complete typing a manuscript. After 2 hours, he was called away. What fractional part of the assignment was left incomplete?
Answer:
(y – 2) / y.

Explanation:
To type a manuscript karthik took y hours.
Therefore his speed in typing = 1/y.
He was called away after 2 hours of typing.
Therefore the work completed = 1/y * 2.
Therefore the remaining work to be completed = 1 – 2/y.
(i.e.) work to be completed = (y-2)/y
Which of the following is larger than 3/5?
(1) ½ (2) 39/50 (3) 7/25 (4) 3/10 (5) 59/100
Answer:
(2)
The number that does not have a reciprocal is ____________.
Answer:
1

Explanation:
One is the only number exists without reciprocal because the reciprocal of one is one itself.
There are 3 persons Sudhir, Arvind, and Gauri. Sudhir lent cars to Arvind and Gauri as many as they had already. After some time Arvind gave as many cars to Sudhir and Gauri as many as they have. After sometime Gauri did the same thing. At the end of this transaction each one of them had 24. Find the cars each originally had.
Answer:
Sudhir had 39 cars, Arvind had 21 cars and Gauri had 12 cars.
A man bought a horse and a cart. If he sold the horse at 10 % loss and the cart at 20 % gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose Rs. 10 in the bargain. The amount paid by him was Rs._______ for the horse and Rs.________ for the cart.

Answer:
Cost price of horse: Rs. 400 &
Cost price of cart: Rs. 200

Explanation:
Let x be the cost of horse & y be the cost of the cart.
10 % of loss in selling horse = 20 % of gain in selling the cart
Therefore (10 / 100) * x = (20 * 100) * y
è x = 2y -----------(1)
5 % of loss in selling the horse is 10 more than the 5 % gain in selling the cart.
Therefore (5 / 100) * x - 10 = (5 / 100) * y

è 5x - 1000 = 5y

Substituting (1)

10y - 1000 = 5y

5y = 1000

y = 200

x = 400 from (1)
For the following, find the next term in the series

6, 24, 60,120, 210 ?

a) 336 b) 366 c) 330 d) 660
Answer :
a) 336

Explanation : The series is 1.2.3, 2.3.4, 3.4.5, 4.5.6, 5.6.7, ..... ( '.' means product)
1, 5, 13, 25 ?
Answer :
41

Explanation : The series is of the form 0^2+1^2, 1^2+2^2,...
0, 5, 8, 17 ?
Answer :
24

Explanation : 1^2-1, 2^2+1, 3^2-1, 4^2+1, 5^2-1
1, 8, 9, 64, 25 ? (Hint : Every successive terms are related)
Answer :
216

Explanation : 1^2, 2^3, 3^2, 4^3, 5^2, 6^3
8,24,12,36,18,54 ?
Answer :
27
71,76,69,74,67,72 ?
Answer :
67
5,9,16,29,54 ?
Answer :
103

Explanation : 5*2-1=9; 9*2-2=16; 16*2-3=29; 29*2-4=54; 54*2-5=103
1,2,4,10,16,40,64 ?(Successive terms are related)

Answer :
200

Explanation : The series is powers of 2 (2^0,2^1,..).
All digits are less than 8. Every second number is in octal number system.
128 should follow 64. 128 base 10 = 200 base 8.
Find the odd man out.

3,5,7,12,13,17,19
Answer :
12

Explanation : All but 12 are odd numbers
2,5,10,17,26,37,50,64
Answer :
64

Explanation : 2+3=5; 5+5=10; 10+7=17; 17+9=26; 26+11=37; 37+13=50; 50+15=65;
105,85,60,30,0,-45,-90
Answer :
0

Explanation : 105-20=85; 85-25=60; 60-30=30; 30-35=-5; -5-40=-45; -45-45=-90;
What is the number of zeros at the end of the product of the numbers from 1 to 100?
Answer :
127
A fast typist can type some matter in 2 hours and a slow typist can type the same in 3 hours. If both type combinely, in how much time will they finish?
Answer :
1 hr 12 min

Explanation : The fast typist's work done in 1 hr = 1/2
The slow typist's work done in 1 hr = 1/3
If they work combinely, work done in 1 hr = 1/2+1/3 = 5/6
So, the work will be completed in 6/5 hours. i.e., 1+1/5 hours = 1hr 12 min
Gavaskar's average in his first 50 innings was 50. After the 51st innings, his average was 51. How many runs did he score in his 51st innings. (supposing that he lost his wicket in his 51st innings)
Answer :
101

Explanation : Total score after 50 innings = 50*50 = 2500
Total score after 51 innings = 51*51 = 2601
So, runs made in the 51st innings = 2601-2500 = 101
If he had not lost his wicket in his 51st innings, he would have scored an unbeaten 50 in his 51st innings.
Out of 80 coins, one is counterfeit. What is the minimum number of weighings needed to find out the counterfeit coin?
Answer : 4
What can you conclude from the statement : All green are blue, all blue are red. ?
(i) some blue are green
(ii) some red are green
(iii) some green are not red
(iv) all red are blue

(a) i or ii but not both
(b) i & ii only
(c) iii or iv but not both
(d) iii & iv
Answer :
(b)
A rectangular plate with length 8 inches, breadth 11 inches and thickness 2 inches is available. What is the length of the circular rod with diameter 8 inches and equal to the volume of the rectangular plate?
Answer :
3.5 inches

Explanation : Volume of the circular rod (cylinder) = Volume of the rectangular plate
(22/7)*4*4*h = 8*11*2
h = 7/2 = 3.5
What is the sum of all numbers between 100 and 1000 which are divisible by 14 ?
Answer :
35392

Explanation : The number closest to 100 which is greater than 100 and divisible by 14 is 112, which is the first term of the series which has to be summed.
The number closest to 1000 which is less than 1000 and divisible by 14 is 994, which is the last term of the series.
112 + 126 + .... + 994 = 14(8+9+ ... + 71) = 35392
If s(a) denotes square root of a, find the value of s(12+s(12+s(12+ ...... upto infinity.

Answer :
4

Explanation : Let x = s(12+s(12+s(12+.....
We can write x = s(12+x). i.e., x^2 = 12 + x. Solving this quadratic equation, we get x = -3 or x=4. Sum cannot be -ve and hence sum = 4.
A cylindrical container has a radius of eight inches with a height of three inches. Compute how many inches should be added to either the radius or height to give the same increase in volume?
Answer :
16/3 inches

Explanation : Let x be the amount of increase. The volume will increase by the same amount if the radius increased or the height is increased.
So, the effect on increasing height is equal to the effect on increasing the radius.
i.e., (22/7)*8*8*(3+x) = (22/7)*(8+x)*(8+x)*3
Solving the quadratic equation we get the x = 0 or 16/3. The possible increase would be by 16/3 inches.
With just six weights and a balance scale, you can weigh any unit number of kgs from 1 to 364. What could be the six weights?
Answer :
1, 3, 9, 27, 81, 243 (All powers of 3)
Diophantus passed one sixth of his life in childhood, one twelfth in youth, and one seventh more as a bachelor; five years after his marriage a son was born who died four years before his father at half his final age. How old is Diophantus?
Answer :
84 years

Explanation : x/6 + x/12 + x/7 + 5 + x/2 + 4 = x
If time at this moment is 9 P.M., what will be the time 23999999992 hours later?
Answer :
1 P.M.

Explanation : 24 billion hours later, it would be 9 P.M. and 8 hours before that it would be 1 P.M.
How big will an angle of one and a half degree look through a glass that magnifies things three times?
Answer :
1 1/2 degrees
Divide 45 into four parts such that when 2 is added to the first part, 2 is subtracted from the second part, 2 is multiplied by the third part and the fourth part is divided by two, all result in the same number.
Answer:
8, 12, 5, 20

Explanation: a + b + c + d =45; a+2 = b-2 = 2c = d/2; a=b-4; c = (b-2)/2; d = 2(b-2); b-4 + b + (b-2)/2 + 2(b-2) = 45;
I drove 60 km at 30 kmph and then an additional 60 km at 50 kmph. Compute my average speed over my 120 km.
Answer :
37 1/2

Explanation : Time reqd for the first 60 km = 120 min.; Time reqd for the second 60 km = 72 min.; Total time reqd = 192 min
Avg speed = (60*120)/192 = 37 1/2
Five executives of European Corporation hold a Conference in Rome

Mr. A converses in Spanish & Italian
Mr. B, a spaniard, knows English also
Mr. C knows English and belongs to Italy
Mr. D converses in French and Spanish
Mr. E , a native of Italy knows French

Which of the following can act as interpreter if Mr. C & Mr. D wish to converse
a) only Mr. A b) Only Mr. B c) Mr. A & Mr. B d) Any of the other three

Answer : d) Any of the other three.

Explanation : From the data given, we can infer the following.
A knows Spanish, Italian
B knows Spanish, English
C knows Italian, English
D knows Spanish, French
E knows Italian, French

To act as an interpreter between C and D, a person has to know one of the combinations Italian&Spanish, Italian&French, English&Spanish, English&French

A, B, and E know atleast one of the combinations.
If a 6th executive is brought in, to be understood by maximum number of original five he should be fluent in

a) English & French b) Italian & Spanish c) English & French d) French & Italian
Answer :
b) Italian & Spanish

Explanation : No of executives who know

i) English is 2
ii) Spanish is 3
iii) Italian is 3
iv) French is 2

Italian & Spanish are spoken by the maximum no of executives. So, if the 6th executive is fluent in Italian & Spanish, he can communicate with all the original five because everybody knows either Spanish or Italian.
What is the sum of the first 25 natural odd numbers?
Answer :
625

Explanation : The sum of the first n natural odd nos is square(n).
1+3 = 4 = square(2) 1+3+5 = 9 = square(3)
If Log2 x - 5 Log x + 6 = 0, then what would the value / values of x be?
Ans. x = e2 or e3.
(1/10)18 - (1/10)20 = ?
(a) 99/1020
(b) 99/10
(c) 0.9
(d) none of these
Ans. (a)
The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member ?
Ans.40 years.
Thirty men take 20 days to complete a job working 9 hours a day. How many hour a day should 40 men work to complete the job?
(a) 8 hrs
(b) 7 1/2 hrs
(c) 7 hrs
(d) 9 hrs
Ans. (b)
Find the smallest number in a GP whose sum is 38 and product 1728
(a) 12
(b) 20
(c) 8
(d) none of these
Ans. (c)
If 2x-y=4 then 6x-3y=?
(a)15
(b)12
(c)18
(d)10
Ans. (b)
Mr. Shah decided to walk down the escalator of a tube station. He found that if he walks down 26 steps, he requires 30 seconds to reach the bottom. However, if he steps down 34 stairs he would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the height of the stair way in steps?
Ans.46 steps.
ABCE is an isosceles trapezoid and ACDE is a rectangle. AB = 10 and EC = 20. What is the length of AE?
Ans. AE = 10.
Can you tender a one rupee note in such a manner that there shall be total 50 coins but none of them would be 2 paise coins.?
Ans. 45 one paisa coins, 2 five paise coins, 2 ten paise coins, and 1 twenty-five paise coins.
If x=y=2z and xyz=256 then what is the value of x?
(a)12
(b)8
(c)16
(d)6
Ans. (b)
Pipe A can fill in 20 minutes and Pipe B in 30 mins and Pipe C can empty the same in 40 mins.If all of them work together, find the time taken to fill the tank
(a) 17 1/7 mins
(b) 20 mins
(c) 8 mins
(d) none of these
Ans. (a)
In the given figure, PA and PB are tangents to the circle at A and B respectively and the chord BC is parallel to tangent PA. If AC = 6 cm, and length of the tangent AP is 9 cm, then what is the length of the chord BC?
Ans. BC = 4 cm.
Three cards are drawn at random from an ordinary pack of cards. Find the probability that they will consist of a king, a queen and an ace.
Ans. 64/2210.
A boat travels 20 kms upstream in 6 hrs and 18 kms downstream in 4 hrs.Find the speed of the boat in still water and the speed of the water current?
(a) 1/2 kmph
(b) 7/12 kmph
(c) 5 kmph
(d) none of these
Ans. (b)
A goat is tied to one corner of a square plot of side 12m by a rope 7m long.Find the area it can graze?
(a) 38.5 sq.m
(b) 155 sq.m
(c) 144 sq.m
(d) 19.25 sq.m
Ans. (a)
A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice. Each cat killed more mice than there were cats. How many cats do you think there were ?
Ans. 991.
The square of a two digit number is divided by half the number. After 36 is added to the quotient, this sum is then divided by 2. The digits of the resulting number are the same as those in the original number, but they are in reverse order. The ten's place of the original number is equal to twice the difference between its digits. What is the number?
Ans. 46