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Pipes and Cistern

Q1:

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 hours
3

C 7 hours

D
7 1 hours
2

ANS:C - 7 hours

(A + B)'s 1 hour's work = 1 + 1 = 9 = 3 .
12 15 60 20
(A + C)'s hour's work = 1 + 1 = 8 = 2 .
12 20 60 15
Part filled in 2 hrs = 3 + 2 = 17 .
20 15 60
Part filled in 6 hrs = 3 x 17 = 17 .
60 20
Remaining part = 1 - 17 = 3 .
20 20
Now, it is the turn of A and B and 3 part is filled by A and B in 1 hour.
20
Total time taken to fill the tank = (6 + 1) hrs = 7 hrs.



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