Question

a
A cistern which has leak in the bottom is
filled in 15 hours. Had there been no leak, it
can be filled in 12 hours. If the cistern is full,
the leak can empty it in:
(a) 20 hour
(b) 60 hour
(c) hour
(d) 46 hour​

Answer 1

Step-by-step explanation:

Let 'F' be the hours in which the cistern can be completely filled without any hole in it & 'E' be the hours in which the hole can empty the cistern when it is completely filled.

Such that : In 1 hour, one-Fth part of the cistern is filled and one-Eth part of the cistern is emptied respectively.

Then 1/F - 1/E = 1/15;

which means in 1 hour one-fifteenth of the cistern is filled having a hole.

And 1/F = 1/12;

which means in 1 hour one-twelfth of the cistern is filled without a hole.

1/12 - 1/E = 1/15

=> 1/E = 1/12-1/15 = 1/60

=> E = 60 hours.

Thus the leak can empty the full cistern in 60 hours.