Two pipes P and Q can fill a cistern in 18 and 24 minutes respectively. Both pipes are opened, but after some time, the slower pipe is closed. The cistern gets filled in 12 minutes from the start. When is the slower pipe closed?

Correct option is A

Given:

Pipe P can fill the cistern in 18 minutes.

Pipe Q can fill the cistern in 24 minutes.

Both pipes are opened simultaneously.

The cistern is filled in 12 minutes from the start.  

Solution:

Let after x minutes before the slower pipe closed
P fill 18 minutes
Q fill 24 minutes
LCM of 18 and 24 = 72
Therefore, efficiency of P = $$\frac{72}{18} = 4$$​​
Efficiency of Q = $$\frac{72}{24 }= 3$$​​
According to the question
Pipe P opened for 12 minutes
Therefore, 4 × 12 + x × 3 = 72
48 + 3x = 72
3x = 24
x = 8 minutes.