Question: Two pipes A and B can fill the tank in 24 and 36 minutes, respectively. Both the pipes are opened together. After how many minutes should the pipe B be turned off, so that the tank be fill in 18 minutes?

Solution:

Given that,

Pipe A fills the tank in 24 minutes.

Pipe B fills the tank in 36 minutes.

Total time to fill the tank = 18 minutes.

Now,

LCM of 24 and 36 = 72 (Total capacity of the tank).

Efficiency of pipe A = 72/24 = 3 units/minute.

Efficiency of pipe B = 72/36 = 2 units/minute.

Let,

pipe B be turned off after x minutes.

Pipe A works for 18 minutes.

Pipe B works for x minutes.

Work done by A in 18 minutes = 3 × 18 = 54 units.

​Work done by B in x minutes = 2x = 2x units.

Total work done = 54 + 2x = 72

⇒ 2x = 72 - 54

⇒ 2x = 18

⇒ x = 18/2

∴ x = 9

∴ Pipe B should be turned off after 9 minutes.