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1) Pipe X can fill 4 times faster than another pipe Y and takes 1 hour less time than pipe Y to fill a cistern. Find when the cistern will be full if only Pipe Y is opened.
a) 20 min
b) 80 min
c) 40 min
d) 45 min
2) P, Q and R are three pipes attached to a cistern. P and Q can fill the tank in 10 minutes and 20 minutes respectively, whereas R0 can empty it in 12 minutes. If P, Q and R are kept open successively for 1 minute each, what time will it take to fill the cistern?
a) 40 minutes
b) 40 ¼ minutes
c) 38 minutes
d) 38 ¼ minutes
3) Two pipes P and Q can fill a cistern in 15 and 30 minutes respectively. If both are opened together, but at the end of 5 minutes the first is turned off. How much longer will the cistern take to fill?
a) 32 minutes
b) 30 minutes
c) 27 minutes
d) 25 minutes
4) Two pipes A and B would fill a tank in 16 and 34 minutes respectively. Both pipes being opened, find when the first pipe must be turned off so that the tank may be just filled in 17 minutes?
a) 10 minutes
b) 5 minutes
c) 9 minutes
d) 8 minutes
5) A cistern which could be filled in 11 hours takes one more hour to fill due to a leakage in the bottom. If the cistern is full in what time will the leak empty it?
a) 150 hours
b) 132 hours
c) 130 hours
d) 110 hours
6) A pipe can fill a cistern in 15 hours whereas the cistern when full can be emptied in 20 hours by a leak. When both pipe and the leak are open when will the cistern be full?
a) 40 hours
b) 30 hours
c) 60 hours
d) 25 hours
7) A cistern had a leak which could empty the cistern in 30 minutes. A tap is opened which can fill 3 litres a minute into the cistern, and it is now emptied in 32 minutes. How many litres does the cistern hold?
a) 480 l
b) 960 l
c) 1120 l
d) 1440 l
8) Two pipes A and B can fill a tank in 15 and 40 minutes respectively and a third pipe C can empty it in 30 minutes. How long will it take to fill the tank if all the three are opened at the same time?
a) 17 1/7 minutes
b) 16 1/7 minutes
c) 10 minutes
d) 12 minutes
9) Pipes P and Q can fill a cistern in 9 and 36 minutes respectively. If they are opened on alternate minutes, find in how many minutes the cistern shall be full?
a) 7 minutes
b) 8 ¾ minutes
c) 7 1/5 minutes
d) 9 2/3 minutes
10) If three taps are opened together, a tank can be filled in 40 hours. One of the taps can fill it in 12 hours and another in 15 hours. How does the third tap work?
a) 8 hours
b) 6 hours
c) -6 hours
d) -8 hours
1) Answer: b)
Let Y can fill the cistern in T min, then time taken by X will be T/4 min.
According to question, T – T/4 = 60 min
T = 80 min
2) Answer: b)
In 3 minutes ( 1/10 + 1/20 – 1/12 ) = 1/15 of the cistern can be filled if all the three pipes are open
Let us assume that the last 2 minutes will be filled by P and R
(1/10 + 1/20) = 3/20
So 17/20 part of the cistern is to be filled by P, Q and R.
Time taken to fill 17/20 part of the cistern = (17/20 ÷ 1/15) x 3 = 38 ¼ minutes
Total time = 40 ¼ minutes
3) Answer: c)
For the first 5 minutes = (1/15 + 1/30) = 3/30 = 1/10
So the rest 9/10 of the cistern is to be filled by Q
Time taken to fill 9/10 of the tank by Q = 9/10 x 30 = 27 minutes
4) Answer: d)
P’s 1 minute work = 1/16
Q’s 1 minute work = 1/34
So in 17 minute work done by Q = 17/34 =1/2
In 17 minutes Q can fill half of the tank. So the rest must be filled by P. P can fill half tank in 8 minutes. So it can be closed in 8 minutes.
5) Answer: b)
Work done by the leak in one hour = (1/11 – 1/12) = 1/132
The leak will empty the cistern in 132 hours.
6) Answer: c)
Work done by pipe in 1 hr = 1/15
Work done by leak in 1 hr = 1/20
Cistern will be full in = 1/15 -1/20 = (4-3)/60 = 1/60 hours
7) Answer: d)
Part of the cistern full in one minute
= 1/30 – 1/32 = (16-15)/480 = 1/480
So the tap can fill in 480 minutes
Now in 480 minutes the tap can push 3 x 480 litres of water. Thus the capacity of the cistern is 1440 litres.
8) Answer: a)
1/15 + 1/40 – 1/30 = (8+3-4)/120 = 7/120
So the cistern will be full in =120/7 = 17 1/7 minutes
9) Answer: c)
P’ 1 min work = 1/9
Q’s 1 min work = 1/36
(P + Q)’s 2 min work = 1/9 + 1/36 = 5/36
Cistern will be full in 36/5 = 7 1/5 minutes
10) Answer: d)
1/12 + 1/15 + 1/x = 1/40
1/40 – 1/12 – 1/15 = 1/x
(3-10-8)/120 = 1/x
1/x = – 15/120
X = -8
-ve sign indicates that it is a leakage. So it can empty the tank in 8 hours.