Three pipes A, B and C can fill a cistern in 36 minutes. After working together for 12 minutes, C is closed and A and B fill the cistern in… — Answer & Discussion

Three pipes A, B and C can fill a cistern in 36 minutes. After working together for 12 minutes, C is closed and A and B fill the cistern in 48 minutes. Find the time in which the cistern can be filled

A61 min
B67 min
C72 min
D76 min

Correct answer: C

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Discussion 1

CCommunity12 Jul 2021

72 min

The part of the tank (A + B + C), working together, will fill in 12 min = 12/36 = 1/3
Hence remaining tank = (1 - 1/3) = 2/3 is filled by (A + B) in 48 min
∴ A + B till the tank in 48x3/2 = 72 min
The part of the C can fill in 1 minute= 1/(A+B+C) - 1/(A+B) = 1/36 - 1/72 = 1/72
So, C can fill the whole tank in 72 minutes.