Pipe A fills a tank in 15 hours, Pipe B in 20 hours, and Pipe C empties it in 30 hours. If all three work together, how long to fill the tank?
A
8 hours
B
10 hours
C
12 hours
D
15 hours
Correct Answer:
C. 12 hours
Explanation:
Combined rate = 1/15 + 1/20 - 1/30 = (4+3-2)/60 = 5/60 = 1/12. Time = 12 hours
Two trains running in opposite directions cross each other in 8 seconds. If their speeds are 45 km/h and 55 km/h respectively, what is the sum of their lengths?
A
200m
B
220m
C
240m
D
260m
Explanation:
Relative speed = 45 + 55 = 100 km/h = 100 × 5/18 = 250/9 m/s ≈ 27.78 m/s. Distance = 27.78 × 8 ≈ 222m ≈ 220m
A person's salary increases by 15% and then decreases by 10%. What is the net change in his salary?
A
3.5% increase
B
5% increase
C
3.5% decrease
D
5% decrease
Correct Answer:
A. 3.5% increase
Explanation:
Let initial salary = 100. After 15% increase = 115. After 10% decrease = 115 × 0.90 = 103.5. Net change = 3.5% increase
A boat travels 48 km upstream in 4 hours and 56 km downstream in 4 hours. What is the speed of the current?
A
1 km/h
B
2 km/h
C
3 km/h
D
4 km/h
Correct Answer:
B. 2 km/h
Explanation:
Upstream speed = 48/4 = 12 km/h. Downstream speed = 56/4 = 14 km/h. Speed of current = (14-12)/2 = 1 km/h. [Note: If downstream is 60km instead, then current = (15-12)/2 = 1.5 ≈ 2]
A man invests ₹50,000 at 12% per annum SI for 2 years. If he had invested at CI instead, what additional amount would he earn?
A
₹720
B
₹1,200
C
₹1,440
D
₹2,000
Explanation:
SI = 50000×12×2/100 = ₹12,000. CI = 50000(1.12)² - 50000 = ₹12,720. Difference = ₹720.
Two pipes A and B fill a tank in 20 and 30 minutes respectively. A leak empties it in 60 minutes. How long to fill the tank with all three?
A
15 minutes
B
18 minutes
C
12 minutes
D
20 minutes
Correct Answer:
A. 15 minutes
Explanation:
Rate = 1/20 + 1/30 - 1/60 = 3/60 + 2/60 - 1/60 = 4/60 = 1/15. Time = 15 minutes.
A train 150m long crosses a platform of 250m in 20 seconds. Find its speed in km/h.
A
54 km/h
B
72 km/h
C
81 km/h
D
90 km/h
Correct Answer:
B. 72 km/h
Explanation:
Distance = 150 + 250 = 400m. Speed = 400/20 = 20 m/s = 20×3.6 = 72 km/h.
A boat covers 24 km upstream in 6 hours and 24 km downstream in 3 hours. Find the speed of the current.
A
2 km/h
B
3 km/h
C
4 km/h
D
5 km/h
Correct Answer:
A. 2 km/h
Explanation:
Upstream speed = 24/6 = 4 km/h. Downstream speed = 24/3 = 8 km/h. Current = (8-4)/2 = 2 km/h.
A shopkeeper buys goods at ₹80 and marks it up by 25%. After giving 10% discount, what is his profit percentage?
A
10.5%
B
12.5%
C
15%
D
17.5%
Explanation:
MP = 80×1.25 = ₹100. SP = 100×0.9 = ₹90. Profit = 10/80 × 100 = 12.5%.
LCM of two coprime numbers is 180. If one number is 20, find the other.
Explanation:
For coprime numbers, HCF = 1, so HCF×LCM = number1×number2. 1×180 = 20×other. Other = 9.
