Question

A tank has inlet pipe which can fill it in 4 minutes. There is also a waste pipe in the tank. When both inlet and waste pipes are opened, the empty tank takes 20 minutes to fill. How long will the waste pipe take to empty the full tank when inlet pipe is closed?
1. 10 minutes
2. 5 minutes
3. 16 minutes
4. 24 minutes

Answer 1

Correct Answer - Option 2 : 5 minutes

Given:

Inlet pipe can fill the tank in 4 minutes

And Inlet and a waste pipe can fill  the tank in 20 minutes

Concept used:

Time ∝ 1/Efficiency

And the efficiency of an outlet pipe is negative

Calculation:

Let the time taken by waste pipe to empty a full tank be x minutes

The efficiency of inlet pipe = 1/4

The efficiency of waste pipe = -1/x

⇒ 1/4 + (-1/x) = 1/20

⇒ (x - 4)/4x = 1/20

⇒ 20x - 80 = 4x

⇒ 16x = 80

⇒ x = 5 minutes

∴ The waste pipe will empty a full tank in 5 minutes.