One pipe can fill the tank in 20 min while another pipe can empty it in 60 min. If both the pipes are operated together. how long will it take to fill the tank completely?

Correct option is D

Given:

One pipe can fill a tank in 20min

Second pipe can empty the tank in 60min

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 one pipe in 1 minute will be $$\frac{Total\ Work}{Total\ time\ } =\frac{1}{20}$$​​

Work done  by second pipe in 1 minute will be $$\frac{Total\ Work}{Total\ time} =\frac{1}{60}$$​

Work done  by both pipes together in 1 minute will be =$$\frac{1}{20} - \frac{1}{60} = \frac{3-1}{60} =\frac{2}{60} =\frac{1}{30}$$​

Tank will be filled by both P and Q working together =$$\frac{total\ work }{work\ done\ in\ 1\ minute}=\frac{1}{\frac{1}{30}}= 30 minutes$$​​