Question

Three pipes, A, B, and C are attached to a tank. A and B can fill it in 20 and 30 minutes respectively while C can empty it in 15 minutes.If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled?

Answer 1

Answer

It will take 120 minutes to fill the tank

Explanation

Let A, B  and C are the three pipes

A and B can fill it in 20 and 30 minutes respectively while C can empty it in 15 minutes.

We have to find the LCM(20, 30 , 15) = 60

So the total work is considered as 60

To calculate efficiency of each pipes in one minute

A ⇒ 60/20 = 3

B ⇒ 60/30 = 2

C ⇒ 60/15 = 1

First open pipe A for one minute 3 out of 60 filled

The open B for 1 minute ,  2 out of 60 filled

After 2 minutes 3/60 + 2/60 = 5/60 of tank become filled

Again C is open 4/60  will empty

After 3 minutes, tank have  5/60 - 4/ 60 = 1/60 filled

In 3 minutes fill 1/60

So it will take 3 x 60  =120 minutes to fill the tank

Answer 2

Pipe A can fill the tank in 20 mins

⇒ 1 min = 1/20 of the tanks

Pipe B can fill the tank in320 mins

⇒ 1 min = 1/30 of the tanks

Pipe C can empty the tank in 15 mins

⇒ 1 min = 1/15 of the tanks

Pipe A, B and C are kept open successively for 1 minute each

Every 3 mins = 1/20 + 1/30 - 1/15 = 1/60 of the tank is filled

Find the time needed to fill the tank:

1/60 of the tank = 3 mins

60/60 of the tank = 3 x 60 = 180 mins

Answer: It takes 180 mins to fill the tank