Pipe a can empty a filled tank in 5.6 hours while pipe b can fill the same tank, when empty, in 7 hours.If pipes a and b are alternatively turned on for an hour each time, starting when the tank is full, how long will it take to empty the tank ?
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Problems on Pipes and Cistern - Solved Examples
1. Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
A.
3
9
17
3917 hours B.
1
13
17
11317 hours
C.
2
8
11
2811 hours D.
4
1
2
412 hours
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answer with explanation
Answer: Option A
Explanation:
Solution 1
Pipes A and B can fill the tank in 5 and 6 hours respectively. Therefore,
part filled by pipe A in 1 hour
=
1
5
=15
part filled by pipe B in 1 hour =
1
6
16
Pipe C can empty the tank in 12 hours. Therefore,
part emptied by pipe C in 1 hour
=
1
12
=112
Net part filled by Pipes A,B,C together in 1 hour
=
1
5
+
1
6
−
1
12
=
17
60
=15+16−112=1760
i.e., the tank can be filled in
60
17
=
3
9
17
6017=3917 hours....