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) 10 hours

Answer 1

Correct option is (c) 90 hours

The cistern is filled in 9 hrs.

∴ In 1 hour, \(\frac 19\)​ part of the cistern will be filled.

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

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

So, in 1 hour \(\frac 19\) − \(\frac 1{10}\)​ part

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

∴ The full cistern will be emptied in \(\frac 1{\frac 1{90}}\) hour = 90 hour.