Pipe A B and C are kept open and together fill a tank in t minutes Pipe A is kept open throughout pi...........

Quant (SSC) Pipes&cistern

Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Furthermore, it is known that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes. How long will it take C alone to fill the tank ?

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Explanation:

A is kept open for all t minutes and fills one-third the tank. Or, A should be able to fill the entire tank in '3t' minutes.
A and B together can fill the tank completely in t minutes.
A alone can fill it in 3t minutes.
A and B together can fill 1/t of the tank in a minute.
A alone can fill 1/3t of the tank in a minute.
So, in a minute, B can fill 1/t - 1/3t = 2/2t
Or, B takes 3t/2 minutes to fill an entire tank.
To fill one-third the tank, B will take t/2 minutes. B is kept open for 10 minutes.
t/2 = t - 10, t = 20 minutes.
A takes 60 minutes to fill the entire tank, B takes 30 minutes to fill the entire tank.
A is kept open for all 20 minutes. B is kept open for 10 minutes.
C, which is kept open for 8 minutes also fills one-third the tank.
Or, C alone can fill the tank in 24 minutes.

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