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Pipe and Cisterns Questions with detailed explanation

Published on Friday, December 25, 2015
Today I am sharing Pipes and Cisterns practice questions. Before solving these questions, I recommend you to go through trick to solve these questions here.

Question 1

A cistern has three pipes A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1,2 and 3 am respectively, when will the cistern be empty?
a) 3 pm
b) 4 pm

c) 5 pm
d) 6 am
e) 7 am

Solution (Option E) 
Hint - Up to 3 am both pipe fill the tank = 2/4 + 1/5 = 7/10 part
Remaining 3/10 part is filled in c hours, then
(1/4 + 1/5 –1/2)x = 3/10 → x = 6h. Cistern is filled at 1am + 6hr = 7am

Question 2

A cistern, when full, is emptied by a waste pipe in 30 min., but if a tap (filling source) is opened, it takes 40 min to empty the cistern. How long the cistern will take to become full when both the pipes are working?
a) 140 min
b) 120 min
c) 160 min
d) 180 min
e) 110 min
Solution (Option A)

Question 3

A cistern can be filled by two pipes A and B in 7 ½ h. Both of them are open for 2½ h and then B is closed. A alone now requires 6 (2/3) h more to fill cistern. How long would A take to fill the cistern working alone?
a) 8h
b) 10h
c) 9h
d) 8½ h
e) None of The Above

Solution (Option B)
Hint - Let the filling time for A and B are FA and FB then both are open for 2½ hr, part filled
5/2 [1/fA + 1/fB] = 5/2 (20 / 15)
Next A is open for 6(2/3), part filled = 20/3 [1/fA]
Since cistern is filled, so
[1/3] + 20/3 × [1/fA] = 1
FA = 10 hrs

Question 4

Two taps A and B can fill a cistern in 12 min and 18 min respectively. They are turned on at the same time. If the tap A is turned off after 4 min, how long will tap B take to fill the rest of the cistern?
a) 8 min
b) 9 min
c) 10 min
d) 7 min
e) 15 min
Solution (Option A)

Question 5

A tap can fill a swimming pool in h hours. What part of the pool is filled in y hours?
a) yh
b) h/y
c) y/h
d) y + h
e) h - y
Solution  (Option C)

Question 6

Two fill pipes A and B can fill a tank in 15 and 12 hours respectively. Pipe B alone is kept open for ¾ of time and both pipes are kept open for remaining time. In how many hours, the tank will be full?
a) 18h
b) 20h
c) 10h
d) 13.5h
e) 8h

Solution (Option C)

Question 7

Two fill pipes A and B can fill a tank in 30 and 20 hours respectively. Pipe B alone is kept open for half the time and both pipes are kept open for the remaining time. In how many hours, the tank will be completely full.
a) 25h
b) 15h
c) 40h
d) 28h
e) 35h
Solution (Option B) 
Hint - B is open for total time, say x hrs. and A is kept open for x/2 hrs.
= (x/2 × 30) + x/20 = total work = 1
x = 15

Question 8

Two taps can fill a tank in 12 and 18 min respectively. Both are kept open for 2 min and the first is turned off. In how many min more will the tank be filled?
a) 15 min
b) 20 min
c) 11 min
d) 13 min
e) 8 min
Solution (Option D)

Question 9

Three taps A, B and C can fill a tank in 12, 15 and 20h respectively. If A is open all the time and B and C are open for one hour each alternatively, the tank will be filled in:
a) 6h
b) 7h
c) 5h
d) 9h
e) None of The Above

Solution  (Option B) 
Hint - Filling by (A + B) in 1st hr 1/12 + 1/15 = 3/20, filling by (A +C) in 2nd hr. = 1/12 + 1/20 = 2/15
Filling done in first 2 hr 3/20 + 2/15 = 17/60 in first 6hr = 17/60 × 3 = 15/60, Rest filling = 1 – 51/60 = 2/15
Now in 7th hr, filling is done by (A + B) in  (3/20)/(3/20) = 1 hour 
Total time = 7 hour 

Question 10

A cistern is filled in 9 hours and it takes 10 hours when there is a leak in its bottom. If the cistern is full, in what time shall the leak empty it?
a) 90h
b) 94h
c) 92h
d) 91h
e) None of The Above

Solution (Option A) 
Hint - Using, T = x(x + p)/p = 9 × 10 / 1 = 90 hrs

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