# When two pipes A & B are opened together, it takes 7.5 minutes to fill a tank. Let C be an emptying pipe. If they all are opened together, it takes 15

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When two pipes A & B are opened together, it takes 7.5 minutes to fill a tank. Let C be an emptying pipe. If they all are opened together, it takes 15 minutes to fill the tank. Find the time taken by C to empty the tank if it is completely filled.
1. 5 min
2. 8 min
3. 11 min
4. 15 min

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Correct Answer - Option 4 : 15 min

Given:

Time taken by A and B to fill the tank = 7.5 minutes

Time taken to fill the tank when A, B and C are opened together = 15 min

Formula:

If the time taken by pipes P1, P2,..Pn to fill a tank is p1, p2, ...pn and the time taken by pipes Q1, Q2, ..., Qn to empty it be q1, q2,..., qn respectively and the total time taken by all the pipes to fill the tank is t.

1/t = (1/p1 + 1/p2 + ... + 1/pn) – (1/q1 + 1/q2 + ... + 1/qn)

Efficiency is inversely proportional to time taken for doing work.

Total work = Efficiency × time

Calculation:

${1 \over 15 }= {1 \over 7.5}- {1 \over C}$

${1 \over C }= {1 \over 7.5}- {1 \over 15}$

C = 15 min

Time taken by Pipe C to empty the tank is 15 min.