Question

A pipe can fill a sump with water in 2 hour . because of a leak .it took 8/3hour to fill the sump .the leak can drain all the water of the sump in ?

Answer 1

Let the first pipe be A and let the leak be B

                                                           A           A+B

                                                           2           8/3

 Total capacity of tank        =                    8

                                                           4          3

As find the total capacity of tank by taking the LCM(2 ,8/3) = 8

where 4 and 3 are capacity of tank filled by A and A+B

A + B = 3

A = 4

So, B = -1   as B is the leak so it is emptying the sump with -1 units in 1 hr

B can empty the sump in  = total capacity/units emptied by B in 1 hr

                                         =  8 / 1

                                       = 8 hrs

Answer 2

The pump can fill the sump in 2 hours

⇒ 1 hour = 1/2 the sump

The pump (with the leak ) can fill the sump in 8/3 hours

⇒ 1 hour = 3/8 of the sump

Find the fraction of water in the sump drained in an hour

1 hour = 1/2 - 3/8 = 1/8 of the sump

Find the number of hours to drain the sump:

1/8 of the sump = 1 hour

8/8 of the sump = 1 x 8 = 8 hours

Answer: It will take 8 hours to drain the sump