Exercise : Pipe & Cistern - General Questions
✔ Pipe & Cistern -
General Questions
1.
Pipe A can fill a tank in 10 hours and Pipe B can fill it in 15 hours. If both are opened together, how much time will they take to fill the tank?
View Answer
Answer: Option A
Explanation:
Explanation:
Efficiency of A = \(1/10\), B = \(1/15\). Combined = \(1/10 + 1/15 = 5/30 = 1/6\). Time = 6 hours.
2.
A cistern is normally filled in 8 hours, but it takes 2 hours longer to fill because of a leak in its bottom. If the cistern is full, in how many hours will the leak empty it?
View Answer
Answer: Option A
Explanation:
Explanation:
Normal rate = \(1/8\). Rate with leak = \(1/10\). Leak rate = \(1/8 - 1/10 = 1/40\). Time = 40 hours.
3.
Two pipes can fill a tank in 20 and 30 minutes respectively. If both are opened together, the tank will be full in how many minutes?
View Answer
Answer: Option A
Explanation:
Explanation:
Total units (LCM) = 60. Efficiencies: 3 and 2. Total = 5. Time = \(60 / 5 = 12\) minutes.
4.
Pipe A fills a tank in 5 hours and Pipe B empties it in 10 hours. If both work together, how long will it take to fill the tank?
View Answer
Answer: Option A
Explanation:
Explanation:
Net efficiency = \(1/5 - 1/10 = 1/10\). Time = 10 hours.
5.
A tap can fill a bucket in 6 minutes and another tap can fill it in 12 minutes. If both are opened, how much time is needed?
View Answer
Answer: Option A
Explanation:
Explanation:
Efficiency = \(1/6 + 1/12 = 3/12 = 1/4\). Time = 4 minutes.
6.
Two pipes A and B can fill a tank in 12 and 16 minutes. Both are opened together, but 4 minutes before the tank is full, pipe A is closed. How much time does it take to fill?
View Answer
Answer: Option A
Explanation:
Explanation:
Let total time be \(x\). \(B\) works for \(x\) mins, \(A\) for \((x-4)\). \((x-4)/12 + x/16 = 1\). Multiply by 48: \(4x - 16 + 3x = 48 \implies 7x = 64 \implies x = 9\frac{1}{7}\) minutes.
7.
A tank has two pipes. Pipe A can fill it in 45 minutes and B can empty it in 1 hour. In what time will the empty tank be full if both are opened?
View Answer
Answer: Option A
Explanation:
Explanation:
Efficiency = \(1/45 - 1/60 = (4-3)/180 = 1/180\). Time = 180 minutes (3 hours).
8.
Three taps A, B, and C can fill a tank in 12, 15, and 20 hours. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in?
View Answer
Answer: Option A
Explanation:
Explanation:
Total = 60. Eff: A=5, B=4, C=3. Hr 1 (A+B) = 9 units. Hr 2 (A+C) = 8 units. 2-hour cycle = 17 units. 3 cycles (6 hrs) = 51 units. Rem = 9. Next hr (A+B) finishes it. Total = 7 hours.
9.
Pipe A can fill a tank in 20 mins and Pipe B in 30 mins. If they are opened for 1 minute alternately, how long will it take to fill?
View Answer
Answer: Option A
Explanation:
Explanation:
Total = 60. Eff: A=3, B=2. 2 mins = 5 units. 12 cycles (24 mins) = 60 units. Time = 24 minutes.
10.
A large tanker can be filled by two pipes A and B in 60 and 40 mins respectively. How many mins does it take to fill the tanker if B is used for half the time and A and B fill it together for the other half?
View Answer
Answer: Option A
Explanation:
Explanation:
Let total time be \(x\). \((A+B)\) works for \(x/2\), \(B\) for \(x/2\). \((x/2)(1/60 + 1/40) + (x/2)(1/40) = 1 \implies (x/2)(5/120) + (x/2)(3/120) = 1 \implies 8x/240 = 1 \implies x = 30\) minutes.