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Home > Arithmetic Aptitude > Pipes and Cistern > Questions and Answers

Exercise:

Exercise 1

01. Two inlet pipes if opened together can fill a tank in 6 minutes. If one pipe takes 5 minutes more than the other pipe to fill the tank, then find the time in which each pipe can fill the tank separately.
A. (20, 15) minutes B. (15, 10) minutes
C. (20, 25) minutes D. None of these

Answer and Explanation

Answer: (15, 10) minutes

Explanation:
Let x be the time in minutes required by pipe A to fill the tank, and y minutes be the time required by pipe B to fill the tank. Also, let pipe A take 5 minutes more than pipe B to fill up the tank.
Therefore, x = y + 5
1/x + 1/y = 1/6
Also, 1/x = 1/(y + 5)
1/(y + 5) + 1/y = 1/6
6*(y + y + 5) = (y + 5)*y
12y + 30 = y2 + 5y
y2 – 7y – 30 = 0
y = 10
x = 15

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02. A inlet pipe can fill a tank in 12 hours and an outlet pipe can empty the tank in 16 hours. If both the pipes are opened simultaneously, find the time taken to fill the tank.
A. 36 hours B. 12 hours
C. 4 hours D. 48 hours

Answer and Explanation

Answer: 48 hours

Explanation:
As the inlet can fill the tank in 12 hours, in one hour it will fill 1/12th of the tank.
Similarly, the outlet pipe in one hour can empty 1/16th part of the tank.
If both are opened simultaneously, the part of the tank filled in one hour is:
1/12 - 1/16 = 1/48
Hence, the tank gets filled in 48 hours.

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03. A leak at the bottom of the tank can empty the tank in 5 hours, while an inlet pipe can fill the same tank at the rate of 6 litres per minute. When the tank is full, the inlet is opened and the tank gets empty in 8 hours due to the leakage. Find the capacity of the tank.
A. 1800 litres B. 3600 litres
C. 4800 litres D. 5760 litres

Answer and Explanation

Answer: 4800 litres

Explanation:
The capacity of the tank is given by C = (p*q*r)/(r – p) litres
Where, p = time in which the leakage can empty the tank in hours = 5 hours
q = rate at which the inlet fills the tank in lph = 6*60 = 360 lph
r = time in which the tank gets emptied in hours = 8 hours
Hence, C = (5*360*8)/(8 – 5)
C = 4800 litres

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04. Pipes P and Q can fill a tank in 20 minutes and 30 minutes respectively. If they are opened simultaneously. In how much time can they fill it?
A. 17 B. 16
C. 12 D. 11

Answer and Explanation

Answer: 12

Explanation:
a pipe takes x hours to fill a tank and another takes y hours to fill it,
=>In xy / x + y hours
=> In this problem, x = 20 and y = 30
=> xy / x + y = 12

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05. Pipes X and Y can fill a tank in 30 minutes and 60 minutes respectively. Both pipes are opened simultaneously. After how much time should X be closed so that the tank is filled in 30 minutes?
A. 44 B. 12
C. 15 D. 34

Answer and Explanation

Answer: 15

Explanation:
Let us say pipe X should be closed after n minutes.
=> i.e. pipe X is in operation for n minutes and pipe Y for all the 30 minutes
=> So, n/30 + 30/60 = t
n = 15

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06. A tank has a leak at its bottom which empties it at 6 litres/minutes. It also has a filling tap which can fill the tank in 6 hours. The tank takes 18 hours to become full. Find the capacity of the tank.
A. 3130 litres  B. 3240 litres
C. 3340 litres D. 3000 litres

Answer and Explanation

Answer: 3240 litres

Explanation:
Explanation: Let the time that would be taken by the leak to empty the full tank be
=>  x hours ,
=> 1/6 – 1/x = 1/18
=> x = 9
Capacity of the tank = (6) (9) (60) = 3240 litres

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07. A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank? 
A. 20 hours B. 25 hours
C. 35 hours D. Cannot be determined
E. None of these

Answer and Explanation

Answer: 35 hours

Explanation:

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08. Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank? 
A. 10 min. 20 sec. B. 11 min. 45 sec
C. 12 min. 30 sec. D. 14 min. 40 sec.

Answer and Explanation

Answer: 14 min. 40 sec.

Explanation:

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09. A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half? 
A. 15 min B. 20 min
C. 27.5 min D. 30 min

Answer and Explanation

Answer: 30 min

Explanation:

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10. Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in: 
A. 6 hours B. 6 2/3 hours
C. 7 hours D. 7 1/2 hours

Answer and Explanation

Answer: 7 hours

Explanation:

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