AMCAT - Aspiring Minds Computer Adaptive Quantitative Ability: Applied Mathematics Questions and Answers 1 — 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?
- 8% (Correct answer)
- 10%
- 12%
- 15%
Correct answer: 8%
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?
- 10 days
- 12 days
- 28/3 days (Correct answer)
- 14 days
Correct answer: 28/3 days
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?
- 250 meters
- 300 meters (Correct answer)
- 200 meters
- 350 meters
Correct answer: 300 meters
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?
- Rs. 1,500
- Rs. 2,700
- Rs. 2,100 (Correct answer)
- Rs. 1,800
Correct answer: Rs. 2,100
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?
- Rs. 650
- Rs. 698 (Correct answer)
- Rs. 700
- Rs. 720
Correct answer: Rs. 698
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.
Question 6: The average age of a class of 30 students is 14 years. If the age of the teacher is included, the average age becomes 15 years. Which of the following is the age of the teacher?
- 44 years
- 31 years
- 45 years
- 46 years (Correct answer)
Correct answer: 46 years
The total age of the 30 students is 30 * 14 = 420 years. When the teacher is included, there are 31 people, and the average age is 15. The total age of the students and the teacher is 31 * 15 = 465 years. The age of the teacher is the difference between these two totals: 465 - 420 = 45 years.
AMCAT - Aspiring Minds Computer Adaptive Quantitative Ability: Applied Mathematics Questions and Answers 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?