Question

Pipes A and B can fill a tank in 18 minutes and 27 minutes, respectively. C is an outlet pipe. When A, B and C are opened together, the empty tank is completely filled in 54 minutes. Pipe C alone can empty the full tank in:
1. 14\(\frac{1}{2}\) minutes
2. 14 minutes
3. 13\(\frac{1}{2}\) minutes
4. 13 minutes

Answer 1

Correct Answer - Option 3 : 13\(\frac{1}{2}\) minutes

Given:

Pipes A and B can fill a tank in 18 minutes and 27 minutes, respectively.

When A, B and C are opened together, the empty tank is completely filled in 54 minutes.

Calculation:

Pipe A's 1 minute's work = 1/18

Pipe B's 1 minute's work = 1/27

Let pipe C's 1 minute's work be 1/C.

⇒ (1/18 + 1/27) - 1/C= 1/54

⇒ 1/C = 2/27

∴ Pipe C can alone empty the tank in 27/2 = 13\(\frac{1}{2}\) minutes.

When a pipe is emptying the tank then it is considered as negative work.