Question

Two pipes A and B can fill a cistern in 20 and 30 minutes respectively,

and a third pipe C can empty it in 40 minutes. How long will it take to fill

the cistern if all the three are opened at the same time?​

Answer 1

Answer:

The tank will be fully filled within 17.14 minutes.

Step-by-step explanation:

Let us suppose, without loss of generality, the full capacity of the tank to be 60 cubic units. Every minute, on average,

• Pipe A fill the tank with 3 cubic units. (60 ÷ 20)
• Pipe B fill the tank with 2 cubic units. (60 ÷ 30)
• Pipe C withdraws 1.5 cubic units of water from the tank.  (60 ÷ 40)

So,

If pipes A, B, and C are opened at the same time,

Then every minute, 3.5 cubic units of water flows into the tank. (3 + 2 - 1.5)

The tank will be fully filled within 17.14 minutes. (60 ÷ 3.5)