Question

There is a leak at the bottom of a cistern. Due to this it takes 8 hours to fill the cistern. Had there not been a leak, it would take one hour less to fill the cistern. How much time does it take for the leak to completely empty the cistern?

Answer 1

Consider the inflow rate of the cistern be x and the volume be V.

Therefore, 8*x = V

Now, let the out flow rate be y

Therefore, 10(x - y) = V

Then, 10x - 10y = 8x

2x = 10y

8x = 40y

Therefore, it takes 40 hours to empty it

Answer 2

The time taken by the leak to completely empty the cistern is 72 hours.

Given: The time required to fill the cistern = 8 hours.

Had there not been a leak, it would take one hour less to fill the cistern.

To Find: The time taken by the leak to completely empty the cistern.

Solution:

The time required to fill cistern without leak = ( 8 + 1 ) hrs = 9 hrs

So, the part of the cistern filled in 1 hr without leak = 1/9

The time required to fill the cistern with leak = 8 hours.

So, the part of the cistern filled in 1 hr with leak = 1/8

So, in one hour, part of the cistern emptied = ( 1/8 - 1/9 )

                                                                  = 1/72

So, the time required to empty the cistern = 1 /( 1/72 ) hours

                                                                         = 72 hours

Hence, the time taken by the leak to completely empty the cistern is 72 hours.

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