Question

A pump can fill a tank with water in 2 hours. Because of a leakage it took 2 \(\frac{1}{3}\) hours to fill the tank. The time taken to empty the full tank due to leakage (in hours) is
1. 8
2. 7
3. 10
4. 14

Answer 1

Correct Answer - Option 4 : 14

Given:

A pump can fill a tank with water in 2 hours

With the leakage, the Pump takes 2 \(\frac{1}{3}\) hours to fill the tank.

Concept Used:

The time taken to fill/empty the tank is inversely proportional to the efficiency.

Calculation:

According to the question,

A pump can fill a tank with water in 2 hours.

The rate of filling the tank by pipe = 1/2

Again, With the leakage, the pipe takes 2 \(\frac{1}{3}\) i.e. 7/3 hours to fill the tank.

Now, According to the concept used :

The rate of filling the tank by pipe along with the leakage will be 3/7.

The rate of leak in the tank = (1/2 - 3/7) = 1/14

Again, According to the Concept used,

The time taken by the leak to empty the tank = 1/(1/14) =  14.

∴ The time taken by the leak to empty the tank is 14 hours.