Question

3. A pipe can fill a cistern in 9 hours. Due to a leak in its bottom, the cistern fills up
10 hours. If the cistern is full, in how much time will it be emptied by the leak?
1
1
Hint. Work done by the leak in 1 hour

​

Answer 1

$\Huge\tt{\color{magenta}{Given:-}}$

A pipe can fill a cistern in 9 hours

Due to a leak in its bottom, the cistern fills up 10 hours

$\Huge\tt{\color{magenta}{To\:Find:-}}$

how much time will it take to emptied by the leak?

$\Huge\tt{\color{magenta}{Solution:-}}$

A pipe can fill a cistern in 9 hrs work done will be=$\sf\dfrac{1}{9}$

A pipe can fill a cistern in 10hrs work done will be=$\sf\dfrac{1}{10}$

Time taken to fill the cistern=Work done in 9hrs - Work done in 10 hrs.

$\sf\longrightarrow \dfrac{1}{9}-\dfrac{1}{10}$

$\sf\longrightarrow \dfrac{10-9}{90}$

$\sf\longrightarrow \dfrac{1}{90}$

So,the cistern will be emptied in 90 hours.