One pipe can fill the tank in 10 minutes while another pipe can empty completely filled tank in 20 minutes. If both the pipes are operated together on empty tank, how long (in minutes) will it take to fill the tank completely?​

Correct option is D

Given:

Inlet pipe fills the tank in 10 minutes.

Outlet pipe empties a full tank in 20 minutes.

Both start together on an empty tank.

Formula Used:

Net rate = fill rate - empty rate.

Time =$$\dfrac{\text{Work}}{\text{Net rate}}$$​​

Solution:
Fill rate =$$\dfrac{1}{10}$$​ tank/min.
Empty rate = $$\dfrac{1}{20}$$​ tank/min.
Net rate =$$\dfrac{1}{10}-\dfrac{1}{20}=\dfrac{1}{20}$$​tank/min.

Time to fill one tank =$$\dfrac{1}{\frac1{20}}=20\text{ minutes}$$​​

Alternate Method:
Assume tank capacity = LCM (10,20) = 20 units.
Inlet fills 20/10=2 units/min; outlet empties 20/20=1 unit/min.
Net = 2-1=1 unit/min.
To fill 20 units $$\implies$$​20/1 = 20 minutes.