A pipe can fill a tank in 10 hours. Due to a leak in the bottom, it fills the tank in 22.5 hours. If the tank is full, then how much time will the leak take to empty it?

Correct option is B

Given:

Filling time without leak = 10 hours

Filling time with leak = 22.5 hours

Solution:

Let leak’s emptying rate = $$\frac{1}{x}$$ 

Now, 

​$$\frac{1}{22.5} = \frac{1}{10} - \frac{1}{x}$$​​

​$$\frac{1}{x} = \frac{1}{10} - \frac{1}{22.5}$$​​

​$$\frac{1}{x} = \frac{22.5 - 10}{225}$$​​

​$$\frac{1}{x}= \frac{12.5}{225}$$​​

​$$\frac{1}{x} = \frac{5}{90}$$​​

​$$\frac{1}{x} = \frac{1}{18}$$​​

x = 18

Thus, The leak will empty the tank in 18 hours. 

Alternate Solution: ​

Total Work = LCM of 10 and 22.5 = 90 units

Filling rate of pipe = $$\frac{90} { 10}$$​ = 9 units/hour

Net filling rate (with leak) = $$\frac{90} { 22.5}$$​ = 4 units/hour

Leak's rate = 9 - 4 = 5 units/hour (removes work)

If leak empties 5 units per hour and tank has 90 units, then:

Time to empty full tank = $$\frac{90}{5} = 18 \text{ hours}$$​​