An electric pump can fill a tank in 5 hours. Due to a leakage in the tank. it takes $$7\frac{1}{2}$$​ hours to fill the tank. How much time will this leak take to empty the full tank if water does not get in or out of the tank through any other point during this period?

Correct option is D

Given:

Time taken by electric pump to fill the tank = 5 hours

Time taken to fill the tank with the leakage = $$7\frac{1}{2}$$​hours

Formula Used:

Let total work to fill the tank be 1.

Then work done by a pipe in 1 hour $$=\frac{1}{Total\ time\ to\ fill}$$​​

Solution:

Work done  by electric pump in 1 hour will be $$\frac{Total\ Work}{Total\ time\ } =\frac{1}{5}$$​​

Work done  by both pump and leakage working together in 1 hour will be $$\frac{Total\ Work}{Total\ time} = \frac{1}{\frac{15}{2}} = \frac{2}{15}$$​​

Then work done by leakage in one hour = $$\frac{2}{15} - \frac{1}{5} = \frac{2-3}{15}$$​​

​$$= - \frac{1}{15}$$​​

Minus sign indicates flow out of tank

Hence time taken by leakage to empty the tank $$=\frac{1}{\frac{1}{15}} = 15 \ hours$$​​