An inlet pipe can fill a water storage tank in 11 hours and an outlet pipe can empty the completely filled tank in 15 hours. If both pipes opened simultaneously. The time taken to fill the empty tank (in hrs) is :

Correct option is B

Given:

Inlet pipe fills the tank in 11 hours.

Outlet pipe empties the tank in 15 hours.

Formula Used:

Filling rate of the inlet pipe = $$\frac{1}{11}$$​ tank per hour.

Emptying rate of the outlet pipe = $$\frac{1}{15}$$​ tank per hour.

Net filling rate when both pipes are open: $$\frac{1}{11} - \frac{1}{15}$$​

Solution:

LCM (11,15) = 165

$$\frac{1}{11} = \frac{15}{165}$$​

​$$\frac{1}{15} = \frac{11}{165}$$​

Net rate = $$\frac{15}{165} - \frac{11}{165} = \frac{4}{165}$$​

Time taken to fill the empty tank:

Time = $$\frac{1}{\text{Net rate}}$$​

$$= \frac{1}{\frac{4}{165}}\\ \ \\= \frac{165}{4}$$ 

= $$41\frac14$$ hours  

Alternate Method: 

Total Efficiency = 15 -11 = 4 

Total time = $$\frac{165}{4}$$ 

= $$41\frac14$$hours ​