AMCAT Quantitative Ability: Applied Mathematics 2 — Questions and Answers
Question 1: A pipe can fill a tank in 12 hours and another pipe can empty it in 18 hours. If both are opened simultaneously, in how many hours will the tank be filled?
- 24 hours
- 36 hours (Correct answer)
- 30 hours
- 20 hours
Correct answer: 36 hours
Fill rate = 1/12 per hour. Empty rate = 1/18 per hour. Net fill rate = 1/12 – 1/18 = 1/36. Time = 36 hours.
Fill rate = 1/12 tank/hr. Empty rate = 1/18 tank/hr. Net rate = 1/12 − 1/18 = 3/36 − 2/36 = 1/36 tank/hr. Time to fill = 36 hours.
Question 2: A train travels at 60 km/h for the first half of the distance and 90 km/h for the second half. What is the average speed?
- 72 km/h (Correct answer)
- 75 km/h
- 70 km/h
- 80 km/h
Correct answer: 72 km/h
Average speed for equal distances = 2v1v2/(v1+v2) = 2×60×90/150 = 72 km/h.
When two equal distances are covered at speeds v1 and v2, average speed = 2v1v2/(v1+v2) = 2×60×90/150 = 10800/150 = 72 km/h.
Question 3: The ages of A and B are in ratio 5:3. After 6 years the ratio becomes 7:5. What is A's current age?
- 15 years (Correct answer)
- 10 years
- 12 years
- 18 years
Correct answer: 15 years
Let A=5x, B=3x. (5x+6)/(3x+6)=7/5 → 25x+30=21x+42 → x=3. A=15.
A=5x, B=3x. After 6 years: (5x+6)/(3x+6)=7/5. Cross multiply: 25x+30=21x+42 → 4x=12 → x=3. A=5×3=15 years.
Question 4: If 8 workers can complete a task in 15 days, how many days will 12 workers take to complete the same task?
- 10 days (Correct answer)
- 12 days
- 8 days
- 9 days
Correct answer: 10 days
Total work = 8×15 = 120 worker-days. With 12 workers: 120/12 = 10 days.
Work = 8 workers × 15 days = 120 worker-days. Time for 12 workers = 120 ÷ 12 = 10 days.
Question 5: The simple interest on a sum for 3 years at 8% per annum is Rs 1440. What is the principal?
- Rs 6000 (Correct answer)
- Rs 5400
- Rs 4800
- Rs 7200
Correct answer: Rs 6000
SI = PRT/100 → 1440 = P×8×3/100 → P = 144000/24 = 6000.
SI = P × 8 × 3 / 100 = 1440. So P = 1440 × 100 / 24 = 144000 / 24 = Rs 6000.
Question 6: A number when divided by 3 leaves remainder 1, and when divided by 4 leaves remainder 2. The smallest such positive number is:
- 10 (Correct answer)
- 22
- 13
- 7
Correct answer: 10
Numbers congruent to 1 mod 3 and 2 mod 4: checking 10: 10÷3=3R1 and 10÷4=2R2. Smallest is 10.
N ≡ 1 (mod 3) and N ≡ 2 (mod 4). Checking: N=10: 10÷3=3R1 (correct), 10÷4=2R2 (correct). Smallest is 10.
AMCAT Quantitative Ability: Applied Mathematics 2
A pipe can fill a tank in 12 hours and another pipe can empty it in 18 hours.
If both are opened simultaneously, in how many hours will the tank be filled?