AMCAT - Aspiring Minds Computer Adaptive Quantitative Ability: Applied Mathematics Questions and Answers

Question 1

A shopkeeper sells a laptop for Rs. 45,000, making a profit of 20%. To attract more customers, he offers a 10% discount on the selling price. What is his new profit percentage?

Accepted Answer

8%

Answer

First, find the cost price (CP) of the laptop. Selling Price (SP) = CP * (1 + Profit%). So, 45000 = CP * (1 + 0.20), which means CP = 45000 / 1.20 = Rs. 37,500. The new selling price after a 10% discount is 45000 * (1 - 0.10) = Rs. 40,500. The new profit is New SP - CP = 40500 - 37500 = Rs. 3,000. The new profit percentage is (New Profit / CP) * 100 = (3000 / 37500) * 100 = 8%.

Question 2

A can complete a piece of work in 15 days and B can complete the same work in 20 days. They start working together, but A leaves after 4 days. In how many days will B complete the remaining work?

Accepted Answer

28/3 days

Answer

A's one day's work is 1/15. B's one day's work is 1/20. Their combined work for one day is (1/15) + (1/20) = (4+3)/60 = 7/60. In 4 days, they complete 4 * (7/60) = 28/60 = 7/15 of the work. The remaining work is 1 - (7/15) = 8/15. B alone will complete the remaining work in (8/15) / (1/20) = (8/15) * 20 = 32/3 = 10 and 2/3 days. The question asks for the remaining days, which is (8/15) of the work divided by B's rate (1/20), which is (8/15) * 20 = 160/15 = 32/3 days.

Question 3

A train traveling at 72 km/hr crosses a platform 200 meters long in 25 seconds. What is the length of the train?

Accepted Answer

300 meters

Answer

First, convert the speed of the train from km/hr to m/s. Speed = 72 * (5/18) = 20 m/s. The total distance covered by the train to cross the platform is the length of the train (L) plus the length of the platform. So, Distance = L + 200. Using the formula Distance = Speed * Time, we get L + 200 = 20 * 25. L + 200 = 500. Therefore, L = 500 - 200 = 300 meters.

Question 4

An amount of money is to be distributed among P, Q, and R in the ratio 5:7:9. If the difference between R's share and P's share is Rs. 1,200, what is Q's share?

Accepted Answer

Rs. 2,100

Answer

Let the shares of P, Q, and R be 5x, 7x, and 9x respectively. According to the problem, the difference between R's share and P's share is Rs. 1,200. So, 9x - 5x = 1200. This simplifies to 4x = 1200, which means x = 300. Q's share is 7x, so Q's share is 7 * 300 = Rs. 2,100.

Question 5

A sum of money invested at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. What is the principal amount?

Accepted Answer

Rs. 698

Answer

The interest for one year is the difference between the amounts after 4 years and 3 years. So, Interest for 1 year = Rs. 854 - Rs. 815 = Rs. 39. The interest for 3 years is 3 * 39 = Rs. 117. The principal amount is the amount after 3 years minus the interest for 3 years. Principal = Rs. 815 - Rs. 117 = Rs. 698.

(AMCAT) Aspiring Minds Computer Adaptive Test Practice Test

(AMCAT) Aspiring Minds Computer Adaptive Test Practice Test

AMCAT - Aspiring Minds Computer Adaptive Quantitative Ability: Applied Mathematics Questions and Answers