An electric pump can fill a tank in 6 hours. Due to a leakage in the tank, it takes 7$$\frac{1}{2}$$ hours to fill the tank. How much time will this leak take to empty the full tank if water does not get in or out of the tank through any other point during this period?​

Correct option is C

Given:

The pump alone fills the tank in 6 hours

The pump + leak together fill it in 7.5 hours  = $$\frac{15}{2}$$​ hours

Formula Used:

Rate = Work / Time

Consider the full tank as 1 unit of work.

Solution:

Let the leak alone empty the tank in t hours.

​$$\frac{1}{6} - \frac{1}{t} = \frac{1}{7.5}$$​​

​$$\frac{1}{t} = \frac{1}{6} - \frac{2}{15} = \frac{5 - 4}{30} = \frac{1}{30}$$​​

t = 30 hours

Alternate Solution:

Total capacity = LCM(6, 7.5) = 30 litres

Rates:

Pump alone: $$\frac{30}{6}$$​ = 5 L/h

Pump + leak: $$\frac{30}{7.5}$$​ = 4 L/h

Leak’s rate = 5 - 4 = 1 L/h

Time for leak to empty 30 L

​$$\frac{30 \text{ L}}{1 \text{ L/h}} = 30 \text{ hours}$$​​