Quantitative Aptitude

Q1. The ages of Shirish and Kunder are in the ratio of 5 : 6. After 8 years the ratio of their ages will be 7 : 8. What is the difference in their ages?   

(a) 4 years 

(b) 8 years 

(c) 10 years 

(d) 12 years 

(e) None of these

Q2. The total of the ages of a class of 75 girls in 1050, the average age of 25 of them is 12 years and that of another 25 is 16 years. Find the average age of the remaining girls.  

(a) 12 years 

(b) 13 years 

(c) 14 years 

(d) 15 years 

(e) None of these

Q3. The ratio of the ages of Anubha and her mother is 1 : 2. After 6 years the ratio of their ages will be 11 : 20. 9 years before, what was the ratio of their ages?  

(a) 3 : 5 

(b) 2 : 7 

(c) 1 : 4 

(d) 2 : 5

(e) None of these

Q4. The ratio of age of Tina and Rakesh is 9 : 10. 10 years ago the ratio of their ages was 4 : 5. What is the present age of Rakesh?  

(a) 25 years 

(b) 20 years 

(c) 30 years 

(d) 24 years 

(e) None of these

Q5. In a family, mother’s age is twice that of daughter’s age. Father is 10 years older than mother. Brother is 20 years younger than his mother and 5 years older than his sister. What is the age of the father?  

(a) 62 years 

(b) 60 years 

(c) 58 years 

(d) 55 years 

(e) None of these

Q6. A man is 3 years older than his wife and four times as old as his son. If the son becomes 15 years old after 3 years, what is the present age of the wife?  

(a) 60 years 

(b) 51 years 

(c) 48 years 

(d) 45 years 

(e) None of these

Q7. After replacing an old member by a new member, it was found that the average age of five members of a club is same as it was 3 years ago. The difference between the ages of the replaced and the new members is: 

(a) 2 years 

(b) 4 years 

(c) 8 years 

(d) 15 years

(e) None of these

Q8. 7 years ago, the ages (in years) of A and B were in the ratio 4 : 5; and 7 years hence they will be in the ratio 5 : 6. The present age of B is: 

(a) 56 years 

(b) 63 years 

(c) 70 years 

(d) 77 years 

(e) None of these

Q9. The age of the father is 30 years more than the son’s age. Ten years hence, the father’s age will become three times the son’s age that time. What is the son’s present age in years?   

(a) Eight  

(b) Seven 

(c) Five 

(d) Cannot be determined 

(e) None of these 

 

Q10. The ratio of the present age of Manoj to that of Wasim is 3 : 11. Wasim is 12 years younger than Rehana. Rehana’s age after 7 years will be 85 years. What is the present age of Manoj’s father, who is 25 years older than Manoj? 

(a) 43 years

(b) 67 years 

(c) 45 years 

(d) 69 years 

(e) None of these 

Q11. The ratio of the present ages of Ram and Rakesh 6 : 11. 4 years ago, the ratio of their ages was 1 : 2. What will be Rakesh’s age after 5 years?   

(a) 45 years  

(b) 29 years 

(c) 49 years 

(d) Cannot be determined 

(e) None of these 

Q12. Radha’s present age is 3 years less than twice her age 12 years ago. Also the ratio of Raj’s present age of Radha’s present age is 4 : 9. What will be Raj’s age after 5 years?  

(a) 12 years 

(b) 7 years 

(c) 21 years 

(d) Cannot be determined 

(e) None of these 

Q13. Ratio of the ages of Priyanka and Sanjay is 7 : 8. 7 years ago, the ratio of their ages was 6 : 7. What is the present age of Sanjay?  

(a) 56 years 

(b) 77 years 

(c) 30 years 

(d) 14 years 

(e) None of these 

Q14. At present, Meena is eight times her daughter’s age. 8 years from now, the ratio of the ages of Meena and her daughter will be 10 : 3. What is Meena’s present age?  

(a) 32 years 

(b) 40 years  

(c) 36 years 

(d) Cannot be determined 

(e) None of these 

Q15. The ages of Ritu and Karan are in the ratio of 4 : 5. After 10 years, the ratio of their ages will be 6 : 7. What is the difference in their ages?  

(a) 4 years 

(b) 6 years 

(c) 10 years 

(d) 5 years 

(e) None of these 

Quantitative Aptitude

Q1. A person invested Rs 4400 in two parts one at 6% and the other at 10% rate of interest. If his overall gain is 9%, find the money invested at 10% interest. 
(a) 4400
(b) 3300
(c) 5500
(d) 3500
(e) 6000

Q2. The average age of P and Q is 20 years. If R were to replace P, the average would be 19 and if R were to replace Q, the average would be 21. What are the age of P, Q and R?
(a) 22, 18, 20
(b) 20, 20, 18
(c) 18, 22, 20
(d) 18, 20, 22
(e) None of these

Q3. 3 years ago, the average age of a family of 5 members was 17 years. With the birth of a new baby, the average age of six members remains the same even today. Find the age of the new baby.
(a) 1 year
(b) 2 year
(c) 3/2 year
(d) 4 year
(e) None of these

Q4. 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
(e) None of these

Q5. David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross?
(a)19
(b)28
(c)30
(d)37
(e) None of these

Q6. In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 66 2/3% of the number of students of 8 years age which is 96. What is the total number of students in the school?
(a) 172
(b) 180
(c) 200
(d) 190
(e) None of these

Q7. If the length, breadth and height of a cuboid is increased by 10%, 20%, 30% respectively. Then find the percentage increase in the volume of the cuboid?
(a) 71.6%
(b) 60%
(c) 171.6%
(d) Can’t be determined
(e) None of these

Q8. By selling 88 meters of cloth a man loses the selling price of 22 meters. Find the loss per cent.
(a) 20%
(b) 25%
(c) 30%
(d) 35%
(e) None of these

Q9. A sells a tube to B at a profit of 25% and B sells it to C at profit of 20%. If C pays Rs 450 for it, what did A pay for it?
(a) Rs 240
(b) Rs 247.5
(c) Rs 300
(d) Rs 500
(e) None of these

Q10. A, B and C started a business investing Rs 9000, 12000, 10000 respectively. A kept the money for whole year. B took his entire amount after 3 months and C with drew 3000 Rs after 3 months. If after a year, the total profit was Rs 7,900, what was A’s share in it?
(a) Rs 4,000
(b) Rs 3,600
(c) Rs 3900
(d) Rs 3500
(e) None of these

Q11. A lent Rs 2500 to B for 4 years and Rs 4000 to C for 3 years on simple interest at the same rate of interest and received Rs 4400 in all from both of them as interest. The rate of interest per annum is:
(a) 25%
(b) 17%
(c) 22%
(d) 20%
(e) None of these

Q12. 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 29 is earned as interest from both the loans. What was the original rate of interest? 
(a) 3.6%
(b) 4.5%
(c) 5%
(d) 3%
(e) None of these

Q13. The difference between the simple interest received from two different sources on Rs 1500 for 3 years is Rs 1.350. The difference between their rates of interest is:
(a) 0.01%
(b) 0.02%
(c) 0.03%
(d) 0.3%
(e) None of these

Q14. An amount of Rs 1,00,000 is invested in two types of shares. The first yields an interest of 9% p.a. and the second, 13% p.a. If the total interest at the end of one year is 10%, then the amount invested in each share was:
(a) Rs 52,500, Rs 47,500
(b) Rs 75,000, Rs 25,000
(c) Rs 72,500, Rs 27,500
(d) Rs 82,500, Rs 17,500
(e) None of these

Q15. Ram purchased a Maruti for Rs 200,000 then, find the difference in the final depreciated values in 2 years for 2 cases, where in one case depreciation is valid for original value and in another case depreciation is valid for remaining value and the rate of depreciation is 10% per year.
(a) Rs 3000
(b) Rs 2000
(c) Rs 1500
(d) Rs 1800   
(e) None of these

SOLUTIONS: 

S2. Ans.(a)

Sol.  Given P + Q = 40 …(i)

R + Q = 38  …(ii)

P + R = 42  …(iii)

Adding all the three equations we have, 

P + Q + R = 60 …(iv)

Solving these equations, we have,

R = 20 years, Q = 18 years and P = 22 years. 

S3. Ans.(b)

Sol.  Sum of present age of the six members = (17 × 6) = 102 years.

Average of the present age of the 5 members (excluding baby) = 17 + 3 = 20 years.

Sum of present ages of the 5 members = 5 × 20 = 100 years.

⇒ Age of the baby = 102 – 100 = 2 years.  

S4. Ans.(b)

Sol.  Suppose the man works overtime for x hours.

Now, working hours in 4 weeks = (5 x 8 x 4) = 160.

  160 x 2.40 + x X 3.20 = 432

  3.20x = 432 - 384 = 48

  x = 15.

Hence, total hours of work = (160 + 15) = 175.

S5. Ans.(c)

Sol.  Suppose their paths cross after x minutes.

Then, 11 + 57x = 51 - 63x         120x = 40

x = 1

3

Number of floors covered by David in (1/3) min. =  1 x 57  = 19.

3

So, their paths cross at (11 +19) i.e., 30th floor.

S6. Ans.(c)

Sol.  Let the number of students be x. Then total number of students of 8 years and above 8 years 

= (100 – 20)% of x = 80% of x

⇒ 80% of x = 96+2/3×96⇒80/100 x=160

⇒ x = 200 

S7. Ans.(a)

Sol.  Initial volume = l × b × h. Increased volume will be equal to 1.1l ×1.2b ×1.3h = 1.716lbh. Therefore percentage increase in volume will be given by the expression ((1.716 -  1)  ×lbh)/lbh×100=71.6%

 

S8. Ans.(a)

Sol.  We know C.P – loss = S.P. Hence we get the relation as, C.P of 88m – S.P. of 22m = S.P of 88m. Hence S.P of 110m = C.P of 88m. Therefore ratio of S.P : C.P :: 4 : 5. Therefore there will be loss and given by loss % =(5 - 4)/5×100=20%.

S9. Ans.(c)

Sol.  Let A paid = Rs x 

120% of 125 % of x = 450 ⇒ 120/100×125/100×x=450

⇒ x = Rs 300 

S10. Ans.(b)

Sol.  In partnership problems profit earned is directly proportional to the product of Investment and Time period for which investment was made in the partnership business.

Required ratio of profit distribution among A, B, and C respectively will be as followed,

= 9 × 12: 12 × 3: 10 × 3 + 7 × 9 = 36: 12:31, 

hence A will get 36/(36 +  12 +  31)×7900= Rs 3600.

S13.   S.13 Ans.(c)

Sol.   Difference of S.I = Rs 1.35 for 3 years, hence difference of SI for 1 year is Rs 0.45 therefore R% of the principal will equal Rs 0.45 or R% of 1500 will be equal to 0.45 or R = 0.03%, where R equals difference of rates. 

\

              S15. Ans.(b)

Sol.  Case 1: Depreciation is valid for original value then total depreciation will be 10% × 2 × 200000 = 40,000

   Case 2:

           If depreciation is valid for remaining value then depreciation for first year will be 10% × 1 × 200000 = 20,000 and depreciation for second year will be 10% × 1 × 180000 = 18,000 and total depreciation will be 38000. Therefore, the difference in the final depreciated values for 2 cases, 

           where in one case depreciation is valid for original value and in another case depreciation is valid for remaining value will be 2000. 

S15.
           

Quantitative Aptitude

Q1. The average weight of 5 apples is 100 g and the average weight of 4 oranges is 80 g. If 2 apples and 2 oranges are picked from them then average weight is found to be 85 g. What is the average weight of the remaining apples and oranges?

(a) 88 g

(b) 90 g

(c) 96 g

(d) 95 g

(e) 92 g

Q2. A person bought 20 kg of rice at Rs. 10.50 per kg and 30 kgs at Rs. 12 per kg. He mixed the two and sold the mixture at Rs. 11.40 per kg. What was the gain in this deal (in Rs.)?

(a) 0

(b) 20

(c) 100

(d) 75

(e) 5

Q3. A vessel of 70 litres is filled with milk and water. 75 percent of milk and 25 percent of water is taken out of the vessel. It is found that the vessel is vacated by 60 percent. Find the initial quantity of water.

(a) 21 litres

(b) 25 litres

(c) 27litres

(d) 32 litres

(e) None of these

Q4. How many litres of fresh water should be mixed with 30 litres of 50% milk solution so that resultant solution is a 10% milk solution?

(a) 120 litres

(b) 25 litres

(c) 150 litres

(d) 60 litres

(e) 160 litres

Q5. How much water should be added to a mixture so that water may be 20 percent of the final mixture?

A. The mixture of milk and water measures 80 litres.

B. It contains 5 percent water initially.

C. It contains 76 litre milk initially.

(a) A alone is sufficient.

(b) B and C together are sufficient.

(c) Any two of the three are sufficient.

(d) A, B and C all the three together are necessary.

(e)All the three even together are not sufficient.

Directions (6-9) Read the passage below and solve the questions based on it:

There are two-brands of TVs, Onida and Videocon in the market. Onida is an old brand launched in 1990 and Videocon is a new brand launched in 1997. For both these brands, 20% of the TVs purchased every year are disposed off as out-dated exactly two years later. It is known that 10 Onida TVs were disposed off in 1997. The following table gives us the number of TVs in operation at the end of the year from 1996 to 2000.

Q6. What is the average number of Videocon TVs disposed every year off by 2000 since its launch?

(a) 4

(b) 12

(c) 8

(d) 10

(e) 7

Q7. What is the average number of Onida TVs purchased every year till 1995?

(a) 20

(b) 24

(c) 28

(d) 32

(e) Cannot be determined

Q8. For which of the following years, average of Onida and Videocon disposed maximum?

(a) 1997

(b) 1998

(c) 1999

(d) 2000

(e) Cannot be determined

Q9. What is the average number of Videocon TVs purchased every year by 2000?

(a) 33.5

(b) 37.5

(c) 40

(d) 35

(e) None of these

Q10. Ranbir purchased 30 kg of rice at the rate of Rs. 17.50 per kg and another 30 kg rice at a certain rate. He mixed the two and sold the entire quantity at the rate of Rs. 18.60 per kg and made 20 per cent overall profit. At what price per kg did he purchase the lot of another 30 kg rice? 

(a) Rs. 14.50 

(b) Rs. 12.50

(c) Rs. 15.50

(d) Rs. 13.50 

(e) None of the above

Q11. The ratio of the quantities of an acid and water in a mixture is 1 : 3. If 5 litres of acid is further added to the mixture, the new ratio becomes 1 : 2. The quantity of new mixture in litres is: 

(a) 32

(b) 40

(c) 42

(d) 45

(e) None of the above

Q12. In three vessels, the ratio of water and milk is 6 : 7, 5 : 9 and 8 : 7, respectively. If the mixture of the three vessels is mixed, then what will be the ratio of water and milk? 

(a) 2431 : 3781   

(b) 3691 : 4499 

(c) 4381 : 5469 

(d) 5469 : 3691 

(e) None of the above

Q13. Two vessels contain milk and water in the ratio 3 : 2 and 7 : 3. Find the ratio in which the contents of the two vessels have to be mixed to get a new mixture in which the ratio of milk and water is 2 : 1.   

(a) 2 : 1

(b) 1 : 2 

(c) 4 : 1 

(d) 1 : 4

(e) None of the above

Q14.  A and B are two alloys of gold and copper prepared by mixing metals in the ratio 7 : 2 and 7 : 11 respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of gold and copper in C will be:  

(a) 5 : 7 

(b) 5 : 9

(c) 7 : 5 

(d) 9 : 5 

(e) None of the above

Q15. There are two vessels A and B. Vessel A is containing 40 litres of pure milk and vessel B is containing 22 litres of pure water. From vessel A, 8 litres of milk is taken out and poured into vessel B. Then 6 litres of mixture (milk and water) is taken out and from vessel B poured into vessel A. What is the ratio of the quantity of pure milk in vessel A to the quantity of pure water in vessel B?  

(a) 14 : 9

(b) 21 : 11

(c) 24 : 13 

(d) 14 : 5 

(e) 21 : 13