Question

A cistern is normally filled in 10 hours. However, it takes 12 hours when there is a leak in its bottom. If the cistern is full, in what time shall the leak empty it?

• A. 10 hours
• B. 15 hours
• C. 30 hours
• D. 60 hours

Answer 1

The correct option is D 60 hours

Filling efficiency of the cistern without leak $=\frac{1}{10}$

Given, It takes 12 hours to empty the tank with leak, which means the efficiency $=\frac{1}{12}$
Let the emptying efficiency be $\frac{1}{x}$
Thus, $\frac{1}{12}=\frac{1}{10}-\frac{1}{x}$
Solving, $x=60$ hours.