__Quantitative Aptitude Word Problems | IBPS | Insurance Exams__**1. Mayur weighs twice as much as Shweta. Shweta’s weight is 60% of Deepika’s weight. Rakesh weighs 50% of Vikas’s weight. Vikas weighs 190% of Mayur’s weight. Which of these people weighs the least ?**

A. Mayur

B. Deepika

C. Shweta

D. Rakesh

**2. Two numbers are in the ratio P : Q. When 1 is added to both the numerator and the denominator, the ratio gets changed to R/S. Again, when 1 is added to both the numerator and the denominator, it becomes 1/2. Find the sum of P and Q.**

A. 3

B. 4

C. 5

D. 6

E. None of these

**3. Ankit and Ganesh each invested Rs 45000 for 3 years at the same rate of interest but Ankit’s investment is compounded annually while Ganesh’s investment is charged on simple interest. What amount did Ankit receive more than Ganesh?**

A. 2040

B. 7800

C. 8500

D. Data insucient

E. None of these

**4. A contractor undertook a work to complete in 90 days. But just after 40 days he observed that only 2/5th of the project work has been completed. To complete the work in time (ie, in rest days) minimum how many workers he had to increase. If there were initially 75 workers were deployed for the task ?**

A. 25

B. 30

C. 15

D. 40

E. 75

**5. Kunal bought a house in Vastu Vihar, whose sale price was Rs 16 lakh. He availed 20% discount as an early bird offer and then 10% discount due to cash payment. After that he spent 10% of the cost price in interior decoration and laws of the house. At what price should he sell the house to earn a pro**

**fi**

**t of 25% ?**

A. 12.78 lakh

B. 15.84 lakh

C. 14.96 lakh

D. 13.54 lakh

E. None of these

**6. The sum of lengths of a train and a platform is 800 meters. The train crosses the platform in 32 seconds and crosses a man standing on platform in 20 seconds. Find the length of the platform.**

A. 200 m

B. 240 m

C. 272 m

D. 300 m

E. 400 m

**7. For every rupee that Ricky invests in simple interest, he also invests 2 rupees in compound interest. The rate of interest in case of simple interest is 12% per annum while for compound interest, it is 10% per annum. The total amount of money invested is Rs. 18000, and it is invested for 3 years. How much interest will be earned in total by Ricky?**

A. Rs. 6132

B. Rs. 6228

C. Rs. 6318

D. Rs. 6000

E. Rs. 6424

**8. The price of a perishable item decreases by 10% every day. Heath bought 20 kg of this item and sold it after 3 days. Still he made a profit of 20% over market price of this item on the day he sold them. If the price of 1 kg of this item was bought for Rs. 120, then at what price all 20 kg of it was sold?**

A. Rs. 2080

B. Rs. 2099.52

C. Rs. 2116.45

D. Rs. 2167.32

E. Rs. 2208.36

**9. P and Q are two points along the flow of a river. R is midpoint of line joining P and Q. Between P and R, speed of river is 2 km/hr. But just after R, speed of river becomes 4 km/hr till Q. The water is flowing from P to Q. The speed of boat in still water is 14 km/hr. If the boat takes 8 hours to cover distance P and Q, then find the distance between P and Q.**

A. 112.67 km

B. 120 km

C. 135.63 km

D. 145.21 km

E. 160 km

**10. Uranium and Thorium are mixed in the ratio 3 : 7 in order to make the mixture ready for nuclear fission. The cost of Uranium is Rs. 30000 per milligram. If the cost of a milligram of mixture is Rs. 25000, then what is the price of a milligram Thorium?**

A. Rs. 20675

B. Rs. 20000

C. Rs. 21672.33

D. Rs. 22857.14

E. Rs. 23168.67

**11. In a family of a husband, wife and son, son is 28 years younger than the father. 3 years back, the ratio of ages of wife and husband was 4 : 5. After 3 years, the ratio of ages of father and son will be 9 : 2. What will be the age of wife after 7 years?**

A. 25 years

B. 28 years

C. 31 years

D. 34 years

E. 40 years

**12. 80 workers are employed to do a work. The work will be finished in 30 days. However, after a few days, 20 workers left the work. After two more days, 20 more workers left. It took 37 days for remaining workers to finish the remaining work. For how many days all 80 workers worked together?**

A. 8

B. 10

C. 12

D. 15

E. 20

**13. A shopkeeper bought 20kg of sugar at Rs. 6 per kg and another 15kg at Rs. 8 per kg. He also mixed the two, If the total selling price was Rs. 265, what is the approximately profit percentage?**

A. 7.41%

B. 8.41%

C. 9.41%

D. 10.41%

E. 11.41%

**14. The average age of 80 boys in a class is 15. The average age of a group of 15 boys in the class is 16 and the average age of another 25 boys in the class is 14. What is the average age of the remaining boys in the class?**

A. 15

B. 16

C. 20

D. 14.5

E. None of these

**15. Kabir was asked to finish testing of an application in 15 days, which is generally completed by him in a span of 20 days. His project manager has asked his colleague, Vikrant to help him in testing the application. This being a new application for Vikarnt, he is only 80% as efficient as Kabir. Working together, they will be able to finish the testing in how many days?**

A. 100/9 days

B. 100/11 days

C. 9/7 days

D. 100/7 days

E. None of these

**Solutions:**

**1. C)**ATQ, M = 2S; S = 0.6D; R = 0.5V; V = 1.9M

From this information we get,

R = 0.5 * 1.9M = 9.5M

V = 1.9M

S = 0.5M

D = 10/6 * 5/10 * M = 5M/6

So, Shweta weighs least since Mayur > Shweta

**2. C)**Let the two original numbers be 1 and x.

Therefore, (1 + 1)/(x + 1) = R/S and 3/(x + 2) = 1/2

By solving the above equations we get x = 4

So, 1/x = P/Q = 1/4

Therefore required sum = 5

**3. D)**As the rate of interest is unknown we can’t determine.

**4. C)**Let total workers be x

Given, the work done initially = 2/5

Remaining work = 3/5

Therefore, 3(40 * 75) = 50 * x * 2

=> x = (3 * 40 * 75)/(2 * 5) = 90

Initial workers = 75

Therefore (90 – 75 = 15) 15 workers should be
increased.

**5. B)**Let the MP be 100.

Then for first discount we get 100 – 20% of 100 = 80

For second discount we get 80 – 10% of 80 = 72 (CP)

Then he spent 10% of CP for house = 72 + 10% of 72 =
79.2

Given Profit should be 25%

=> SP = 125% of CP = 1.25 * 79.2 = 99

100 ≡ 1600000

Then 99 = (1600000 * 99)/100 = 1584000 = Rs.15.84
lakh

**6. D)**Let the length of plateform be P meters. So, length of train will be (800 – P) meters.

When train crosses platform, distance covered is sum
of lengths of train and platform.

The train crosses the platform in 32 seconds.

We know, Time taken = Distance/speed

⇒ 32 = 800/speed of train

⇒ Speed of train = 25 m/sec

The train crosses a man standing on platform in 20
seconds.

When train crosses a man, distance covered is length
of train.

⇒ 20 = (800 – P)/25

⇒ P = 800 – 500 = 300 meters

∴ Length of platform is 300 meters.

**7. A)**For every rupee that Ricky invests in simple interest, he also invests 2 rupees in compound interest.

Suppose he invests Rs. T in simple interest and Rs.
2T in compound interest.

Total amount invested is Rs. 18000.

⇒ T + 2T = 18000

⇒ T = 18000/3 = 6000

⇒ Amount invested in simple interest is Rs.
6000 and in compound interest is Rs. 12000.

The rate of interest in case of simple interest is
12% per annum while for compound interest, it is 10% per annum.

We know, Simple interest = (Principal × Rate ×
Time)/100

And, Compound Interest = P × [(1 + R/100)^T – 1]

⇒ Total interest earned in 3 years = (6000 × 12 × 3)/100 +
12000 × [(1+10/100)

^{3}– 1]
⇒ Total interest earned in 3 years = 2160 +
12000 × 0.331 =
2160 + 3972 = 6132

∴ Total interest earned is Rs. 6132.

**8. B)**It is given that 1 kg of item was bought for Rs. 120. Price decreases by 10% every day.

After 3 days, market price of 1 kg of item = Rs. 120
× (1-10/100) × (1-10/100) × (1-10/100) = Rs. 87.48

If Heath made a profit of 20% over market price on
the day he sold,

Selling Price = Cost price × (1 + (Profit %)/100)

⇒ Selling price = 87.48 × (1 + 20/100) = 87.48
× 1.2 = 104.976

⇒ 1 kg of item was sold for Rs. 104.976.

∴ Price for which 20 kg of item was sold = Rs.
104.976 × 20 = Rs.
2099.52

**9. C)**Let the distance between P and Q be T km.

Since river flows from P to Q, going from P to Q
means going downstream.

Downstream speed between P and R = (14 + 2) km/hr =
16 km/hr

Downstream speed between R and Q = (14 + 4) km/hr =
18 km/hr

Since R is midpoint of P and Q, distance from P to R
will be T/2 km and between R and Q will be T/2 km.

Time taken to go from P to Q = (T/2)/16 + (T/2)/18 =
8

⇒ T/32 + T/36 = 8

⇒ 17T/288 = 8

⇒ T = 2304/17 = 135.53

∴ Distance between P and Q is 135.63 km.

**10. D)**Let the price of a milligram of Thorium be Rs. T.

Let amounts of Uranium and Thorium mixed be 3D
milligram and 7D milligram, respectively.

Price of resultant mixture = [Price of 3D milligram
of Uranium + Price of 7D milligram of Thorium]/(3D + 7D)

⇒ 25000 = [3D × 30000 + 7D × T]/10D

⇒ 250000 = 90000 + 7T

⇒ T = 160000/7 = 22857.14

∴ Price of a milligram of Thorium is Rs.
22857.14.

**11. D)**Let the age of wife be T years, and that of father be M years.

⇒ Age of son = (M – 28) years

After 3 years, the ratio of ages of father and son
will be 9:2.

⇒ (M+3)/(M – 28 + 3) = 9/2

⇒ 2M + 6 = 9M – 225

⇒ M = 231/7 = 33

3 years back, the ratio of ages of wife and husband
was 4:5.

⇒ (T – 3)/(M – 3) = 4/5

⇒ T – 3 = (30 × 4)/5 = 24

⇒ T = 27

Present age of wife is 27 years.

∴ After 7 years, age of wife will be 34 years.

**12. B)**Let us suppose that 80 workers worked for N days.

⇒ Workers for the first N days = 80

Workers for next 2 days = 80 – 20 = 60

Workers from next 37 days = 60 -20 = 40

80 workers can finish work in 30 days.

Number of man days required to finish work = 80 × 30
= 2400

⇒ 80 × N + 60 × 2 + 40 × 37 = 2400

⇒ 80N = 2400 – 1480 – 120 = 800

⇒ N = 10

∴ For 10 days, 80 workers worked.

**13. D)**Total C.P. = 20 × 6 + 15 × 8 = 120 + 120 = 240

Total S.P. = 265

Profit % = (265 – 240)/240 × 100 = 250/24 = 10.41%

**14. E)**Average age of the remaining boys = [(80 * 15) – (15 * 16 + 25 * 14)]/40 = (1200 – 500)/40 = 15.25

Hence, the required answer is 15.25

**15. A)**Kabir takes 20 days to complete the work.

Vikrant is 80% as efficient as Kabir. Therefore, he
can do the same work in 25 Days.

Working together, they can complete the work in =1/20+1/25
=9/100 =100/9days