Question

A cistern which could be filled in $9$ hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full, in what time will the leak empty it ?

• A. $19$ hours
• B. $1$ hours
• C. $90$ hours
• D. $\frac{3}{5}$ hours

Answer 1

The correct option is C $90$ hours

The cistern is filled in $9$ hrs.

$\therefore$ In $1$ hour, $\frac{1}{9}$ part of the cistern will be filled.

Again, it takes $(9+1)$ hours $=10$ hrs. to fill the cistern due to a leak.

$\therefore$ In $1$ hour, $\frac{1}{10}$ part of the cistern will be filled when it leakes.

So, in $1$ hour $\frac{1}{9}-\frac{1}{10}$ part

$=$ $\frac{1}{90}$ part will be emptied.

$\therefore$ The full cistern will be emptied in $\frac{1}{\frac{1}{90}}$ hour $=90$ hour.