A pipe can fill a tank in 9 hours. Another pipe can empty the filled tank in 12 hours. If both the pipes are opened simultaneously, then the time (in hours) in which the tank will be two-third filled, is:

Correct option is A

Given:

Filling pipe time = 9 hours

Emptying pipe time = 12 hours

Required: Time to fill two-third of the tank when both pipes operate together

Solution: ​

Filling Rate =$$\frac{1}{9}$$​,   Emptying Rate = $$\frac{1}{12}$$​​

Net Rate = $$\frac{1}{9} - \frac{1}{12} = \frac{4 - 3}{36} = \frac{1}{36}$$​​

Time to fill $$\frac{2}{3}$$​of the tank:

​$$= \frac{2}{3} \div \frac{1}{36} = \frac{2}{3} \times 36 = 24 \, \text{hours}$$​​

Thus, The tank will be two-third filled in 24 hours. 

Alternate Solution:  

Total work = Efficiency $$\times$$​ time

LCM of 9 and 12 = 36 units assumed total capacity

Pipe A fills = $$\frac{36}{9}$$​ = 4 units/hr

Pipe B empties = $$\frac{36}{12}$$​ = 3 units/hr

Net rate = 4 - 3 = 1 unit/hr

To fill $$\frac{2}{3}$$​of tank;

​$$= \frac{2}{3} \times 36 = 24 \text{ units}$$​​

Time = $$\frac{24}{1} = 24 \text{ hours}$$​​

Thus, The tank will be two-third filled in 24 hours