Question

a full tank in 8 hrs. When the tank is full, a tap is opened into the tank which intakes water at rate of 6 liter per hour and the tank is now emptied in 12hrs. What is the capacity of the tank?

Answer 1

Given that the leak can empty a full tank in 8 hrs.

Therefore the work done by it in 1 hour = 1/8 hrs.

Given that the tank is emptied by the leak in 12 hrs.

Therefore the work done by it in 1 hour = 1/12 hrs.

The total part filled in 1 hour = 1/8 - 1/12

                                               = 1/24.

Therefore the time is taken to fill the tank = 24 hours.

Given that the tap fills the water at the rate of 6 liters per hour.

Therefore the capacity of the tank = 24 * 6

                                                           = 144 litres.



Hope this helps!

Answer 2

A leak can empty the tank in 8hrs.
Therefore let one hour work be=1/8

Another leak can empty the tank in 12hrs.
Therefore let one hour work be=1/12

Now we need to subtract both of them as both the leak's empty the tank..

Therefore 1/8-1/12 = 1/24

Therefore both the leak's can together empty the tank in 24 hours.

But Given,
It takes water at 6litre/hr

As the tank was emptied in 24 hours now it can be refilled at 6litre/hr..
Therefore, 24×6 =144

Therefore the capacity of the tank is 144 litres.

Hope this helps!