Two pipes P and Q can fill a tank in 32 minutes and 48 minutes. Both pipes are opened and after some time pipe Q is turned off. The tank is filled in 24 minutes. When was the pipe Q closed?

Correct option is A

Given:

Time taken by Pipe P to fill the tank alone = 32 minutes

Time taken by Pipe Q to fill the tank alone = 48 minutes

Total time taken to fill the tank = 24 minutes

Solution:

Rate of filling by P = $$\frac{1}{32}$$​​

Rate of filling by Q = $$\frac{1}{48}$$​​

Let the time after which pipe Q was closed be t minutes.

Equation: Total water filled = Water filled by both pipes for t minutes+ Water filled by P alone for the remaining time

​$$\frac{t}{32} + \frac{t}{48} + \frac{24 - t}{32} = 1$$  

​$$\frac{3t +2t + 72 - 3t }{96} = 1$$ 

$$\frac{2t + 72}{96} = 1$$

2t = 96 - 72 

t = 12 

After 12 minutes the pipes Q closed.