Question

A water tank can be emptied in 40 minutes by a pipe of d 'diameter, so how long will it take for a 2d diameter pipe to be emptied?
1. 20 min
2. 10 min
3. 40 min
4. 80 min

Answer 1

Correct Answer - Option 2 : 10 min

Given:

A pipe of diameter d can empty the tank in 40 minutes

Formula used:

Area of a circle = πr²

Work done = Time × Efficiency

Calculation:

Total work done by the pipe with the diameter d

40 × π(d/2)² = 10πd²

Now the diameter is doubled

So the time to empty the tank is

Time = \(\dfrac{10πd^2}{\pi (\frac{2d}{2})^2}\)

⇒ Time = 10 minutes

∴ The pipe with double the diameter will empty the tank in 10 minutes.