Two pipes A and B can fill a tank in 12 hours and 15 hours respectively If they are opened on altern...........

Quant (SSC) Pipes&cistern

Two pipes A and B can fill a tank in 12 hours and 15 hours respectively. If they are opened on alternate hours with pipe A opened first, then in how many hours the tank will be full?

13 hrs

14 1/2 hrs

12 hrs

12 1/2 hrs

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Explanation:

A = 12 hours, B = 15 hours
Total work = LCM(12,15) = 60
So efficiency of A = 60/12 = 5,
efficiency of B = 60/15 = 4
2 hrs work of (A+B) = 5+4 = 9
2*6(12) hours work of (A+B) = 9*6 = 54
So remaining work = 60-54 = 6
Now A’s turn at 13th hour,
he will do remaining work(6) in 6/12 hr
So total 12 1/2 hrs