Two pipes A and B can fill the tank in 40 and 60 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 30 minutes?

Question: Two pipes A and B can fill the tank in 40 and 60 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 30 minutes?

Solution:
Given that,
Pipe A fills the tank in 40 minutes.
Pipe B fills the tank in 60 minutes.
Total time to fill the tank = 30 minutes.

Now,
LCM of 40 and 60 = 120 (Total capacity of the tank).
Efficiency of pipe A = 120 / 40 = 3 units/minute.
Efficiency of pipe B = 120 / 60 = 2 units/minute.

Let,
pipe B be turned off after x minutes.
Pipe A works for 30 minutes.
Pipe B works for x minutes.

Work done by A in 30 minutes = 3 × 30 = 90 units.
Work done by B in x minutes = 2 × x = 2x units.

Total work done = 90 + 2x = 120.
⇒ 2x = 120 - 90.
⇒ 2x = 30.
⇒ x = 30 / 2.
⇒ x = 15
Pipe B should be turned off after 15 minutes.