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Two inlet pipes A and B and an outlet pipe C together can fill a tank in 15 minutes and pipes A and C together can empty that tank completely in 30 minutes. If time taken by pipes B and C together to fill that tank is 1 hour, then what is the time taken by pipes A and B together to fill that tank?

Two inlet pipes A and B and an outlet pipe C together can fill a tank in 15 minutes and pipes A and C together can empty that tank completely in 30 minutes. If time taken by pipes B and C together to fill that tank is 1 hour, then what is the time taken by pipes A and B together to fill that tank? Correct Answer 12 minutes

Let capacity of tank = LCM of (15, 30 and 60) = 60 units

The efficiency of A + B + C = 4 units      -----(1)

The efficiency of A + C = 2 units      ----(2)

The efficiency of B + C = 1 units      ----(3)

Putting (3) in (1), we get

A = 3 units

Hence, from (2) C = -1 units and from (3) B = 2 units

Hence, combined efficiency of A and B = 5 units

∴ Time taken = 60/5 = 12 minutes

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