Question

two pipes a and b can fill a cistern in 20 and 30 minutes respectively, and a third pipe c can empty it in 40 minutes. how long will it take to fill the cistern if all the three are opened at the same time?

Answer 1

Hope this solution will help you

Answer 2

It takes 17 minutes to fill the cistern if all the three are opened at the same time

Solution:

Given that,

Work done by pipe A in 1 minute = $\frac{1}{20}$

Work done by pipe B in 1 minute = $\frac{1}{30}$

Work done by pipe C in 1 minute = $-\frac{1}{40}$

If all are opened, then,

$\rightarrow \frac{1}{20} + \frac{1}{30} - \frac{1}{40}\\\\\rightarrow \frac{6+4-3}{120}\\\\\rightarrow \frac{7}{120}$

Then, time taken to fill the tank is:

$Time\ taken = \frac{120}{7} = 17.14 \approx 17$

Thus, it takes 17 minutes to fill the cistern if all the three are opened at the same time

Learn more:

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