A tap can fill a Tank in 16 hours. Due to a hole in its base it is filled in 24 hours, If tank is full then in how many hours it will be empty through the hole.

Correct option is D

Given:
Time taken by tap to fill the tank = 16 hours
Time taken to fill tank with hole = 24 hours

Concept Used:

The rate of work of each person is the reciprocal of the time they take to complete the work. example,
A complete work in x day,
Rate of work in one day = $$\frac{1}{x}$$​ day

Solution:

Let the hole alone empty the full tank in x hours.

Combined work = Tap's work − Hole's work.

​$$\frac{1}{16} - \frac{1}{x} = \frac{1}{24}$$

​$$\frac{1}{x} = \frac{1}{16} - \frac{1}{24}$$​

​$$\frac{1}{x} = \frac{3 - 2}{48} = \frac{1}{48}$$​
x = 48​​

So, The hole alone can empty the full tank in 48 hours.

Thus, the correct answer is (d).

Alternative Method:

Time = $$\frac{48}{1} = 48$$ hours​