Pipes A and B can fill an empty cistern in 13 minutes and 39 minutes, respectively. Both Pipe A and Pipe B are opened together. After how much time should Pipe A be turned off so that the empty cistern is completely filled in a total of 27 minutes?

Correct option is C

Given:

Pipe A can fill the cistern in 13 minutes.

Pipe B can fill the cistern in 39 minutes.

The cistern should be filled in a total of 27 minutes.

Solution:
Let the time for which Pipe A works be t minutes, and Pipe B works for 27 minutes.

The work done is based on the rate of filling for each pipe.

Rate of Pipe A =$$\frac{1}{13}$$​ cistern per minute.

Rate of Pipe B =$$\frac{1}{39}$$​ cistern per minute.

The total work done in 27 minutes is 1 cistern, so the equation is:

​$$\left( \frac{1}{13} \times t \right) + \left( \frac{1}{39} \times 27 \right) = 1$$​

​$$\left( \frac{1}{13} \times t \right) + \frac{9}{13} = 1 \\ \ \\ \frac{t}{13} + \frac{9}{13} = 1\\ \ \\ \frac{t}{13} = 1 - \frac{9}{13} = \frac{4}{13}$$​​

t = 4

So, Pipe A should be turned off after 4 minutes.