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Pipes and Cistern - Aptitude Questions and Answers - RejinpaulPlacement




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1.
Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
Answer & Solution
Answer: b) 20 hours

Solution:   Part filled by A in i hour = 1/36;

Part filled by B in 1 hour = 1/45

Part filled by (A + B) in 1 hour = [(1/36) + (1/45)] = 9/180 = 1/20

Hence, both the pipes together will fill the tank in 20 hours
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2.
Two pipes can fill a tank in 10 hours and 12 hours respectively while a third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time will the tank be filled?
Answer & Solution
Answer: d) 7 hours 30 minutes

Solution:   Net part filled in 1 hour = [(1/10) + (1/12) - (1/20)] = 8/60 = 2/12

The tank will be full in 15/2 hrs = 7 hours 30 minutes
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3.
If two pipes function simultaneously, the reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours does it take the second pipe to fill the reservoir?
Answer & Solution
Answer: c) 30 hrs

Solution:   Let the reservoir be filled by first pipe in x hours.

Then, second pipe will fill it in (x + 10) hours.

(1/x) + [1 / (x + 10)] = 1/12

=> [(x + 10 + x) / {x (x + 10)} ] = 1/12

=> (x^2) - 14x - 120 = 0

=> (x - 20)(x + 6) = 0

=> x = 20    {neglecting the -ve value of x}

So, the second pipe will take (20 + 10) hrs, i.e; 30 hrs to fill the reservoir
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4.
A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waster pipe in the cistern. When all the three are opened, the empty cistern is full in 20 minutes. How long will the waste pipe take to empty the full cistern?
Answer & Solution
Answer: b) 10 minutes

Solution:   Work done by the waste pipe in 1 minute = (1/20) - [(1/12) + (1/15)] = -(1/10)     {-ve sign means emptying}

Waste pipe will empty the full cistern in 10 minutes
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5.
An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3  1/2 hours to fill the tank. If the tank is full, how much time will the leak take to empty it?
Answer & Solution
Answer: d) 21 hours

Solution:   Work done by the leak in 1hour = [(1/3) - {1 / (7/2)} ] = [(1/3) - (2/7)] = 1/21

The leak will empty the tank in 21 hours
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6.
Two pipes can fill a cistern in 14 hours and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom it took 32 minutes more to fill the cistern. When the cistern is full, in what time will the leak empty it?
Answer & Solution
Answer: c) 112 hours

Solution:   Work done by the two pipes in 1 hour = [(1/14) + (1/16)] = 15/112

Time taken by these pipes to fill the tank = 112/15 hours = 7 hrs 28 min

Due to leakage, time taken = 7 hrs 28 min + 32 min = 8 hrs

Work done by (two pipes + leak) in 1 hour = 1/8

Work done by the leak in 1 hour = [(15/112) - (1/8)] = 1/112

Leak will empty the full cistern in 112 hours.
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7.
Two pipes A and B can fill a tank in 36 min. and 45 min. respectively. A water pipe C can empty the tank in 30 min. First A and B are opened. After 7 minutes, C is also opened. In how much time, the tank is full?
Answer & Solution
Answer: b) 46 min

Solution:   Part filled in 7 min. = 7 [(1/36) + (1/45)] = 7/20

Remaining part = [1 - (7/20)] = 13/20

Net part filled in 1 min. when A, B, and C are opened = [(1/36) + (1/45) - (1/30)] = 1/60

Now, 1/60 part is filled in 1 min.

13/20 part is filled in [60 * (13/20)] = 39 min.

Total time taken to fill the tank = (39 + 7) min. 46 min.
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