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. Find t?
  • a)
    18
  • b)
    36
  • c)
    27
  • d)
    24
Correct answer is option 'D'. Can you explain this answer?

Civil Engineering (CE) Question

Rachika Grewal answered Aug 03, 2018
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 1t of the tank in a minute. A alone can fill 13t of the tank in a minute. So, in a minute, B can fill 1t−13t=23t. Or, B takes 3t2 minutes to fill an entire tank.

To fill one-third the tank, B will take t2 minutes. B is kept open for t - 10 minutes.

t2 = 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. Choice (D)

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