Exercise : Pipe & Cistern - General Questions
✔ Pipe & Cistern -
General Questions
21.
Two pipes fill a cistern in 15 and 12 hours. A third pipe empties it in 4 hours. If the pipes are opened at 8, 9, and 11 AM, when will it be empty?
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Answer: Option A
Explanation:
Explanation:
At 11 AM: A (3 hrs) = 3/15, B (2 hrs) = 2/12. Total = \(1/5 + 1/6 = 11/30\). Net rate = \(1/15 + 1/12 - 1/4 = -1/10\). Time to empty = \((11/30) / (1/10) = 11/3 = 3\) hrs 40 mins. 11 AM + 3:40 = 2:40 PM.
22.
Pipe A is 4 times faster than B and takes 45 mins less to fill a tank. What is the time if both are open?
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Answer: Option A
Explanation:
Explanation:
Eff A:B = \(4:1\). Time A:B = \(1:4\). Diff = 3 units \(\to\) 45 mins. 1 unit = 15 mins. A=15, B=60. Combined = \(1/15 + 1/60 = 5/60 = 1/12\). Time = 12 minutes.
23.
A leak in the bottom of a tank can empty it in 6 hours. A pipe fills water at 4 L/min. When the tank is full, the tap is opened and the tank is emptied in 8 hours. What is the capacity?
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Answer: Option A
Explanation:
Explanation:
Leak = \(-1/6\). Combined = \(-1/8\). Tap = \(-1/8 - (-1/6) = 1/24\) per hour. Capacity = \(24 \text{ hrs} \times 60 \text{ min} \times 4 \text{ L/min} = 5,760\) liters.
24.
A tank is filled by 3 pipes A, B, and C. C is twice as fast as B and B is twice as fast as A. If A and B fill it in 32 mins, how long for all three?
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Answer: Option A
Explanation:
Explanation:
Eff A=1, B=2, C=4. \((A+B)\) eff = 3. Total work = \(3 \times 32 = 96\) units. Combined eff (A+B+C) = 7. Time = \(96 / 7 = 13\frac{5}{7}\) minutes.
25.
Pipes A and B can fill a tank in 20 and 30 hrs. Both pipes are opened but when the tank is \(1/3\) full, a leak develops which admits \(1/3\) of the water supplied by both pipes. What is the total time?
View Answer
Answer: Option A
Explanation:
Explanation:
Total = 60. Eff: A=3, B=2. Phase 1 (\(1/3\) full = 20 units): Time = \(20/5 = 4\) hours. Phase 2 (Rem 40 units): New eff = \(5 - (1/3) \times 5 = 10/3\). Time = \(40 / (10/3) = 12\) hours. Total = \(4 + 12 = 16\) hours.