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Thursday 7 August 2014

A magician holds one  six- sides die in his left hand and two in his right. what is the probability the number of dice in his left hand is greater than the sum of of the dice in his right. ?
PROPERTIES OF POLYGON

Tuesday 15 July 2014

DATA SUFFICIENCY

1. What is the speed of the train whose length is 210 metres?
I. The train crosses another train (Howrah Express/12869) of 300 metres length running in opposite direction in 10 seconds.
II. The train crosses another train (Howrah Express/12869) running in the same direction at the speed of 60 km/hr in 30 seconds.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Ans - E

2. What is the length of a running train crossing another 180 metre long train running in the opposite direction?
I. The relative speed of the two trains was 150 kmph.
II. The trains took 9 seconds to cross each other.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Ans - E

3. What is the length of a running train?
I. The train crosses a man in 9 seconds.
II. The train crosses a 240 metre long platform in 24 seconds.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Ans - E

4. 8 men and 14 women are working together in a field. After working for 3 days, 5 men and 8 women leave the work. How many more days will be required to complete the work?
I. 19 men and 12 women together can complete the work in 18 days.
II. 16 men can complete two-third of the work in 16 days.
III. In 1 day, the work done by three men in equal to the work done by four women.
A. I only
B. II only
C. III only
D. I or II or III
E. II or III only
Ans - D

5. How many marks did Tarun secure in English?
I. The average mark obtained by Tarun in four subjects including English is 60.
II. The total marks obtained by him in English and Mathematics together are 170.
III. The total marks obtained by him in Mathematics and Science together are 180.
A. I and II only
B. II and III only
C. I and III only
D. All I, II and III
E. None of these
Ans - E

6. In a cricket team, the average age of eleven players in 28 years. What is the age of the captain?
I. The captain is eleven years older than the youngest player.
II. The average age of 10 players, other than the captain is 27.3 years.
III. Leaving aside the captain and the youngest player, the average ages of three groups of three players each are 25 years, 28 years and 30 years respectively.
A. Any two of the three
B. All I, II and III
C. II only or I and III only
D. II and III only
E. None of these
Ans - C

7. Two towns are connected by railway. Can you find the distance between them?
I. The speed of the mail train is 12 km/hr more than that of an express train.
II. A mail train takes 40 minutes less than an express train to cover the distance.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Ans - D

8. The towns A, B and C are on a straight line. Town C is between A and B. The distance from A to B is 100 km. How far is A from C?
I. The distance from A to B is 25% more than the distance from C to B.
II. The distance from A to C is  of the distance C to B.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Ans - C

9. Two cars pass each other in opposite direction. How long would they take to be 500 km apart?
I. The sum of their speeds is 135 km/hr.
II. The difference of their speed is 25 km/hr.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Ans - A

10. How much time did X take to reach the destination?
I. The ratio between the speed of X and Y is 3 : 4.
II. Y takes 36 minutes to reach the same destination.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Ans - E

Sunday 13 July 2014

IMPORTANT FORMULAS : PIPES AND CISTERN

Inlet:
A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.

Outlet:
A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.
If a pipe can fill a tank in x hours, then:
part filled in 1 hour = 1/x
If a pipe can empty a tank in y hours, then:
part emptied in 1 hour = 1/y
If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then
the net part filled in 1 hour = (1/x - 1/y)
If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where x > y), then on opening both the pipes, then
the net part emptied in 1 hour = (1/y - 1/x)

Thursday 10 July 2014

DATA SUFFICIENCY

1. What is the number?
I. The sum of the two digits is 8. The ratio of the two digits is 1 : 3.
II. The product of the two digit of a number is 12. The quotient of two digits is 3.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Ans - C

2. What is the two-digit number?
I. The difference between the two digits is 9.
II. The sum of the digits is equal to the difference between the two digits.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Ans - E

3. What is the two-digit number whose first digit is a and the second digit is b?. The number is greater than 9.
I. The number is multiple of 51.
II. The sum of the digits a and b is 6.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Ans - A

4. A shopkeeper sells some articles at the profit of 25% on the original price. What is the exact amount of profit? To find the answer, which of the following information given in Statements I and II is/are necessary?
I. Sale price of the article
II. Number of articles sold
A. Only I is necessary
B. Only II is necessary
C. Either I or II is necessary
D. Both I and II are necessary
E. None of these
Ans - D

5. A shopkeeper sells some toys at Rs. 250 each. What percent profit does he make? To find the answer, which of the following information given in Statements I and II is/are necessary?
I. Number of toys sold.
II. Cost price of each toy.
A. Only I is necessary
B. Only II is necessary
C. Both I and II are necessary
D. Either I or II ins necessary
E. None of these
Ans - B

6. A man mixes two types of rice (X and Y) and sells the mixture at the rate of Rs. 17 per kg. Find his profit percentage.
I. The rate of X is Rs. 20 per kg.
II. The rate of Y is Rs. 13 per kg.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Ans - D

7. By selling a product with 20% profit, how much profit was earned?
I. The difference between cost and selling price is Rs. 40.
II. The selling price is 120 percent of the cost price.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Ans - A

8. What is Arun's present age?
I. Five years ago, Arun's age was double that of his son's age at that time.
II. Present ages of Arun and his son are in the ratio of 11 : 6 respectively.
III. Five years hence, the respective ratio of Arun's age and his son's age will become 12 : 7.
A. Only I and II
B. Only II and III
C. Only I and III
D. Any two of the three
E. None of these
Ans - D

9.What is Ravi's present age?
I. The present age of Ravi is half of that of his father.
II. After 5 years, the ratio of Ravi's age to that of his father's age will be 6 : 11.
III. Ravi is 5 years younger than his brother.
A. I and II only
B. II and III only
C. I and III only
D. All I, II and III
E. Even with all the three statements answer cannot be determined.
Ans - A

10. What is the present age of Tanya?
I. The ratio between the present ages of Tanya and her brother Rahul is 3 : 4 respectively.
II. After 5 years the ratio between the ages of Tanya and Rahul will be 4 : 5.
III. Rahul is 5 years older than Tanya.
A. I and II only
B. II and III only
C. I and III only
D. All I, II and III
E. Any two of the three
Ans - E

Wednesday 9 July 2014

TIME AND DISTANCE : IMPORTANT FORMULAS

Speed, Time and Distance:
Speed = Distance/Time
Time = Distance/ speed
Distance = (Speed x Time)

km/hr to m/sec conversion:
x km/hr = x X (5/18) m/sec.

m/sec to km/hr conversion:
x m/sec = x X (18/5) km/hr.

If the ratio of the speeds of A and B is a : b, then the ratio of the
the times taken by then to cover the same distance is 1/a : 1/b or b : a.

Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then,
the average speed during the whole journey is: [2xy/(x + y)] km/hr.

Sunday 6 July 2014

TIME AND WORK: IMPORTANT FORMULAS

Work from Days:
If A can do a piece of work in n days, then A's 1 day's work =1/n

Days from Work:
If A's 1 day's work =1/n,then A can finish the work in n days.

Ratio:
If A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3 : 1.

Ratio of times taken by A and B to finish a work = 1 : 3.

Thursday 3 July 2014

PROBABILITY : IMPORTANT FORMULAS

Experiment:
An operation which can produce some well-defined outcomes is called an experiment.

Random Experiment:
An experiment in which all possible outcomes are know and the exact output cannot be predicted in advance, is called a random experiment.

Examples:
# Rolling an unbiased dice.
# Tossing a fair coin.
# Drawing a card from a pack of well-shuffled cards.
# Picking up a ball of certain colour from a bag containing balls of different colours.

Details:
[1] When we throw a coin, then either a Head (H) or a Tail (T) appears.

[2] A dice is a solid cube, having 6 faces, marked 1, 2, 3, 4, 5, 6 respectively. When we throw a die, the outcome is the number that appears on its upper face.

[3] A pack of cards has 52 cards.
It has 13 cards of each suit, name Spades, Clubs, Hearts and Diamonds.
Cards of spades and clubs are black cards.
Cards of hearts and diamonds are red cards.
There are 4 honours of each unit.
There are Kings, Queens and Jacks. These are all called face cards.

Sample Space:
When we perform an experiment, then the set S of all possible outcomes is called the sample space.

Examples:
[1] In tossing a coin, S = {H, T}

[2] If two coins are tossed, the S = {HH, HT, TH, TT}.

[3] In rolling a dice, we have, S = {1, 2, 3, 4, 5, 6}.

Event:
Any subset of a sample space is called an event.

Probability of Occurrence of an Event:
Let S be the sample and let E be an event.
Then, E  S.
P(E) = n(E)/n(S)

Results on Probability:
[1] P(S) = 1
[2] 0  P (E)  1
[3] P() = 0
For any events A and B we have : P(A  B) = P(A) + P(B) - P(A  B)
If A denotes (not-A), then P(A) = 1 - P(A).

Tuesday 1 July 2014

DATA SUFFICIENCY

1. A shopkeeper sells some articles at the profit of 25% on the original price. What is the exact amount of profit? To find the answer, which of the following information given in Statements I and II is/are necessary?
I. Sale price of the article
II. Number of articles sold
A. Only I is necessary
B. Only II is necessary
C. Either I or II is necessary
D. Both I and II are necessary
E. None of these
Ans - D

2. A shopkeeper sells some toys at Rs. 250 each. What percent profit does he make? To find the answer, which of the following information given in Statements I and II is/are necessary?
I. Number of toys sold.
II. Cost price of each toy.
A. Only I is necessary
B. Only II is necessary
C. Both I and II are necessary
D. Either I or II ins necessary
E. None of these
Ans - B

3. A man mixes two types of rice (X and Y) and sells the mixture at the rate of Rs. 17 per kg. Find his profit percentage.
I. The rate of X is Rs. 20 per kg.
II. The rate of Y is Rs. 13 per kg.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Ans - D

4. By selling a product with 20% profit, how much profit was earned?
I. The difference between cost and selling price is Rs. 40.
II. The selling price is 120 percent of the cost price.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Ans - A

5. By selling an article what is the profit percent gained?
I. 5% discount is given on list price.
II. If discount is not given, 20% profit is gained.
III. The cost price of the articles is Rs. 5000.
A. Only I and II
B. Only II and II
C. Only I and III
D. All I, II and III
E. None of these
Ans - A

6. What was the percentage of discount given?
I. 23.5% profit was earned by selling an almirah for Rs. 12,350.
II. If there were no discount, the earned profit would have been 30%.
III. The cost price of the almirah was Rs. 10,000.
A. Only I and II
B. Only II and III
C. Only I and III
D. Any two of the three
E. None of these
Ans - E

7. What is the percent profit earned by the shopkeeper on selling the articles in his shop?
I. Labeled price of the articles sold was 130% of the cost price.
II. Cost price of each article was Rs. 550.
III. A discount of 10% on labeled price was offered.
A. Only I
B. Only II
C. I and III
D. All the three are required
E.Question cannot be answer even with information in all the three statements.
Ans - C

8. What is Sonia's present age?
I. Sonia's present age is five times Deepak's present age.
II. Five years ago her age was twenty-five times Deepak's age at that time.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Ans - E

9. Average age of employees working in a department is 30 years. In the next year, ten workers will retire. What will be the average age in the next year?
I. Retirement age is 60 years.
II. There are 50 employees in the department.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Ans - E

10. Divya is twice as old as Shruti. What is the difference in their ages?
I. Five years hence, the ratio of their ages would be 9 : 5.
II. Ten years back, the ratio of their ages was 3 : 1.
A. I alone sufficient while II alone not sufficient to answer
B. II alone sufficient while I alone not sufficient to answer
C. Either I or II alone sufficient to answer
D. Both I and II are not sufficient to answer
E. Both I and II are necessary to answer
Ans - C

Sunday 29 June 2014

PARTNERSHIP: IMPORTANT FORMULAS

Partnership:
When two or more than two persons run a business jointly, they are called partners and the deal is known as partnership.

Ratio of Divisions of Gains:
When investments of all the partners are for the same time, the gain or loss is distributed among the partners in the ratio of their investments.
Suppose A and B invest Rs. x and Rs. y respectively for a year in a business, then at the end of the year:
(A's share of profit) : (B's share of profit) = x : y.

When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital x number of units of time). Now gain or loss is divided in the ratio of these capitals.
Suppose A invests Rs. x for p months and B invests Rs. y for q months then,
(A's share of profit) : (B's share of profit)= xp : yq.

Working and Sleeping Partners:
A partner who manages the the business is known as a working partner and the one who simply invests the money is a sleeping partner.

Thursday 26 June 2014

RATIO AND PROPORTION: IMPORTANT FORMULAS

[1] Ratio:
The ratio of two quantities a and b in the same units, is the fraction a/b and we write it as a : b.
In the ratio a : b, we call a as the first term or antecedent and b, the second term or consequent.

Eg. The ratio 5 : 9 represents 5/9 with antecedent = 5, consequent = 9.
Rule: The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.
Eg. 4 : 5 = 8 : 10 = 12 : 15. Also, 4 : 6 = 2 : 3.

[2] Proportion:
The equality of two ratios is called proportion.
If a : b = c : d, we write a : b :: c : d and we say that a, b, c, d are in proportion.
Here a and d are called extremes, while b and c are called mean terms.
Product of means = Product of extremes.
Thus, a : b :: c : d  (b x c) = (a x d).

[3] Fourth Proportional:
If a : b = c : d, then d is called the fourth proportional to a, b, c.
Third Proportional:
a : b = c : d, then c is called the third proportion to a and b.
Mean Proportional:
Mean proportional between a and b is root of ab.

[4] Comparison of Ratios:
We say that (a : b) > (c : d) = a/b > c/d  
Compounded Ratio:
The compounded ratio of the ratios: (a : b), (c : d), (e : f) is (ace : bdf).

[5] Duplicate Ratios:
Duplicate ratio of (a : b) is (a2 : b2).
Sub-duplicate ratio of (a : b) is (a : b).
Triplicate ratio of (a : b) is (a3 : b3).
Sub-triplicate ratio of (a : b) is (a1/3 : b1/3).
If a/b =c/d, then (a+b)/(a-b) = (c+d)/ (c-d)[componendo and dividendo]

[6] Variations:
We say that x is directly proportional to y, if x = ky for some constant k and we write, x is proportional to y.
We say that x is inversely proportional to y, if xy = k for some constant k and
we write,  x is inversely proportional y.

Tuesday 24 June 2014

PROBLEMS ON AVERAGE

Q. 1. All of the following are examples of real security and privacy risks EXCEPT :
(1) Hackers
(2) Spam
(3) Viruses
(4) Identity theft
(5) None of these
Ans - 2

Q.2. A process known as --------------- is used by large retailers to study trends.
(1) Data mining
(2) Data selection
(3) POS
(4) Data conversion
(5) None of these
Ans - 1

Q.3.Which of the following is NOT one of the four major data processing functions of a computer ?
(1) Gathering data
(2) processing data into information
(3) Analyzing the data or information
(4) Storing the data or information
(5) None of these
Ans - 3

Q.4. Is the study of molecules and structures whose size ranges from 1 to 100 nanometers.
(1) Nanoscience
(2) Microelectrodes
(3) Computer forensics
(4)   Artificial intelligence
(5)   None of these
Ans - 1

Q.5. ---------------- is data that has been organized or presented in a meaningful fashion.
(1) A process
(2) Software
(3) Storage
(4) Information
(5) None of these
Ans - 4

Q.6.Computer gather data, which means that they allow users to -------------- data.
(1) Present
(2)  Input
(3) Output
(4) Store
(5) None of these
Ans - 2

Q. 7.After a picture has been taken with a digital camera and processed appropriately, the actual print of the picture is considered :
(1) Data
(2) Output
(3) Input
(4) The process
(5) None of these
Ans - 2

Q. 8. Computers use the ----------- language to process data.
(1) Processing
(2) Kilobyte
(3) Binary
(4)  Representational
(5) None of these
Ans - 3

Q.9. Computers process data into information by working exculsively with :
(1) Multimedia
(2) Words
(3) Characters
(4) Numbers
(5) None of these
Ans - 4

Q.10. In the binary language each letter of the alphabet, each number and each special character is made up of a unique combination of .
(1) Eight bytes
(2) Eight kilobytes
(3) Eight character
(4) Eight bits
(5) None of these
Ans - 4

Sunday 22 June 2014

ALLIGATION OR MIXTURES


[1] Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
A. Rs. 169.50
B. Rs. 170
C. Rs. 175.50
D. Rs. 180
Ans - C

[2] A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?
A. 10
B. 20
C. 21
D. 25
Ans - C

[3] A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
A. 4 litres, 8 litres
B. 6 litres, 6 litres
C. 5 litres, 7 litres
D. 7 litres, 5 litres
Ans - B

[4] In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
A. 3 : 7
B. 5 : 7
C. 7 : 3
D. 7 : 5
Ans - C

[5] How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg?
A. 36 kg
B. 42 kg
C. 54 kg
D. 63 kg
Ans - D

[6] A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
A. 26.34 litres
B. 27.36 litres
C. 28 litres
D. 29.16 litres
Ans - D

[7] In what ratio must water be mixed with milk to gain 16% on selling the mixture at cost price?
A. 1 : 6
B. 6 : 1
C. 2 : 3
D. 4 : 3
Ans - A

[8] Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.
A. 1 : 3
B. 2 : 3
C. 3 : 4
D. 4 : 5
Ans - B

[9] In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10%?
A. 3 : 2
B. 3 : 4
C. 3 : 5
D. 4 : 5
Ans - A

[10] The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is:
A. Rs. 18
B. Rs. 18.50
C. Rs. 19
D. Rs. 19.50
Ans - A

Thursday 19 June 2014

PROBLEMS ON AGES


[1] The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
A. 4 years
B. 8 years
C. 10 years
D. None of these
Ans - A

[2] A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
A. 14 years
B. 19 years
C. 33 years
D. 38 years
Ans - A

[3] A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
A. 7
B. 8
C. 9
D. 10
E. 11
Ans - D

[4] Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
A. 24
B. 27
C. 40
D. Cannot be determined
E. None of these
Ans - A

[5] A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
A. 14 years
B. 18 years
C. 20 years
D. 22 years
Ans - D

[6] Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
A. 16 years
B. 18 years
C. 20 years
D. Cannot be determined
E. None of these
Ans - A

[7] The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:
A. 12 years
B. 14 years
C. 18 years
D. 20 years
Ans - D

[8] At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?
A. 12 years
B. 15 years
C. 19 and half
D. 21 years
Ans - B

[9] Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?
A. 16 years
B. 18 years
C. 28 years
D. 24.5 years
E. None of these
Ans - D

[10] The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
A. 8, 20, 28
B. 16, 28, 36
C. 20, 35, 45
D. None of these
Ans - B

Tuesday 17 June 2014

PROFIT AND LOSS

[1] The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:
A. 15
B. 16
C. 18
D. 25
Ans - B

[2] In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
A. 30%
B. 70%
C. 100%
D. 250%
Ans - B

[3] A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?
A. 3
B. 4
C. 5
D. 6
Ans - C

[4] The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
A. Rs. 2000
B. Rs. 2200
C. Rs. 2400
D. Data inadequate
Ans - A

[5] A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?
A. Rs. 18.20
B. Rs. 70
C. Rs. 72
D. Rs. 88.25
Ans - C

[6] A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?
A. Rs. 1090
B. Rs. 1160
C. Rs. 1190
D. Rs. 1202
Ans - C

[7] Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
A. 3.5
B. 4.5
C. 5.6
D. 6.5
Ans - C

[8] On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:
A. Rs. 45
B. Rs. 50
C. Rs. 55
D. Rs. 60
Ans - D

[9] When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?
A. Rs. 21,000
B. Rs. 22,500
C. Rs. 25,300
D. Rs. 25,800
Ans - C

[10] A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
A. No profit, no loss
B. 5%
C. 8%
D. 10%
E. None of these
Ans - B

Sunday 15 June 2014

PROBLEMS ON PARTERNERSHIP

1. A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is:
A. Rs. 1425
B. Rs. 1500
C. Rs. 1537.50
D. Rs. 1576
Ans - B

2.  A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.
A. Rs. 1900
B. Rs. 2660
C. Rs. 2800
D. Rs. 2840
Ans - B

3. A, B and C enter into a partnership in the ratio 7/2 : 4/3 : 6/5. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then B's share in the profit is:
A. Rs. 2100
B. Rs. 2400
C. Rs. 3600
D. Rs. 4000
Ans - D

4. A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:
A. Rs. 8400
B. Rs. 11,900
C. Rs. 13,600
D. Rs. 14,700
Ans - D

5. Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
A. 5 : 7 : 8
B. 20 : 49 : 64
C. 38 : 28 : 21
D. None of these
Ans - B

6. A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?
A. Rs. 7500
B. Rs. 8000
C. Rs. 8500
D. Rs. 9000
Ans - D

7. A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew 1/4  of his capital and B withdrew 1/5 of his capital. The gain at the end of 10 months was Rs. 760. A's share in this profit is:
A. Rs. 330
B. Rs. 360
C. Rs. 380
D. Rs. 430
Ans - A

8. A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
A. 3 : 5 : 2
B. 3 : 5 : 5
C. 6 : 10 : 5
D. Data inadequate
Ans - C

9.  A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
A. Rs. 45
B. Rs. 50
C. Rs. 55
D. Rs. 60
Ans - A

10. A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
A. Rs. 7500
B. Rs. 9000
C. Rs. 9500
D. Rs. 10,000
Ans - A

Thursday 12 June 2014

SIMPLIFICATION

1. A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
A. 45
B. 60
C. 75
D. 90
Ans - D

2. There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
A. 20
B. 80
C. 100
D. 200
Ans - C

3. The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
A. Rs. 3500
B. Rs. 3750
C. Rs. 3840
D. Rs. 3900
Ans - D 

4. If a - b = 3 and a2 + b2 = 29, find the value of ab.
A. 10
B. 12
C. 15
D. 18
Ans - A

5. The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
A. Rs. 1200
B. Rs. 2400
C. Rs. 4800
D. Cannot be determined
E. None of these
Ans - B

6. One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
A. Rs. 30,000
B. Rs. 50,000
C. Rs. 60,000
D. Rs. 90,000
Ans - C

7. A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:
A. 30 birds
B. 60 birds
C. 72 birds
D. 90 birds
Ans - A

8. To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?
A. 10
B. 35
C. 62.5
D. Cannot be determined
E. None of these
Ans - C

9. In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
A. 160
B. 175
C. 180
D. 195
Ans - B

10. Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ?
A. 256
B. 432
C. 512
D. 640
Ans - C

Tuesday 10 June 2014

RATIO AND PROPORTION

[1]  Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
A. 2 : 5
B. 3 : 5
C. 4 : 5
D. 6 : 7
Ans - C

[2] A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
A. Rs. 500
B. Rs. 1500
C. Rs. 2000
D. None of these
Ans - C 

[3] Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
A. 2 : 3 : 4
B. 6 : 7 : 8
C. 6 : 8 : 9
D. None of these
Ans - A
 
[4] In a mixture 60 litres, the ratio of milk and water 2 : 1. If the this ratio is to be 1 : 2, then the quanity of water to be further added is:
A. 20 litres
B. 30 litres
C. 40 litres
D. 60 litr
Ans - D

[5] The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
A.  8 : 9
B. 17 : 18
C. 21 : 22
D. Cannot be determined
Ans -  C

[6] Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?
A. Rs. 17,000
B. Rs. 20,000
C. Rs. 25,500
D. Rs. 38,000
Ans - D 

[7] If 0.75 : x :: 5 : 8, then x is equal to:
A. 1.12
B. 1.2
C. 1.25
D. 1.30
Ans - B 
 
[8] The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:
A. 20
B. 30
C. 48
D. 58
Ans - B 

[9] The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?
A. 3 : 3 : 10
B. 10 : 11 : 20
C. 23 : 33 : 60
D. Cannot be determined
Ans - C

[10] If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
A. 2 : 5
B. 3 : 7
C. 5 : 3
D. 7 : 3
Ans - C

Sunday 8 June 2014

PROBLEMS ON SIMPLE INTEREST

[1] A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
A. Rs. 650
B. Rs. 690
C. Rs. 698
D. Rs. 700
Ans -   C

[2] Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?
A. Rs. 6400
B. Rs. 6500
C. Rs. 7200
D. Rs. 7500
E. None of these
Ans - A

[3]  A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
A. Rs. 4462.50
B. Rs. 8032.50
C. Rs. 8900
D. Rs. 8925
E. None of these
Ans - D

[4] How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
A. 3.5 years
B. 4 years
C. 4.5 years
D. 5 years
Ans - B

[5] Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
A. 3.6
B. 6
C. 18
D. Cannot be determined
E. None of these
Ans - B

[6] A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?
A. 3%
B. 4%
C. 5%
D. 6%
E. None of these
Ans - D

[7] An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:
A. 10%
B. 10.25%
C. 10.5%
D. None of these
Ans - B

[8] A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:
A. 5%
B. 7%
C. 6%
D. 10%
Ans - D

[9] A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?
A. 3.6%
B. 4.5%
C. 5%
D. 6%
E. None of these
Ans - E

[10] A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:
A. Rs. 2000
B. Rs. 10,000
C. Rs. 15,000
D. Rs. 20,00
Ans - C

Friday 6 June 2014

PROBLEMS ON PERCENTAGE

[1] If 20% of a = b, then b% of 20 is the same as:
A. 4% of a
B. 5% of a
C. 20% of a
D. None of these
Ans- A

[2] Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
A. 2 : 3
B. 1 : 1
C. 3 : 4
D. 4 : 3
Ans - D

[3] In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:
A. 2700
B. 2900
C. 3000
D. 3100
Ans - A

[4] Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
A. 57%
B. 60%
C. 65%
D. 90%
Ans - A

[5] Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
A. Rs. 200
B. Rs. 250
C. Rs. 300
D. None of these
Ans - B

[6] What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
A. 1
B. 14
C. 20
D. 21
Ans - C

[7] If A = x% of y and B = y% of x, then which of the following is true?
A. A is smaller than B.
B. A is greater than B
C. Relationship between A and B cannot be determined.
D. If x is smaller than y, then A is greater than B.
E. None of these
Ans - E

[8] Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:
A. 39, 30
B. 41, 32
C. 42, 33
D. 43, 34
Ans - C

[9] A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
A. 588 apples
B. 600 apples
C. 672 apples
D. 700 apples
Ans - D

[10] Rajeev buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.
A. Rs. 6876.10
B. Rs. 6999.20
C. Rs. 6654
D. Rs. 7000
Ans - A