Question

A large tank can be filled with water in 15 hours. The same tank can be emptied by a drain pipe and 25 hours. If the drain pipe is open while the tank is being filled, how long does it take to fill the tank?

Answer 1

It take 37.5 hours to fill the tank

Explanation:

Given:

Time Taken to fill the tank = 15 hours

Time Taken to empty the tank = 25 hours

To Find:

Time taken to fill the tank when both the inlet and outlet is opened at the same time = ?

Solution:

Let the time to fill the tank be x

In 15 hours the tap fills the tank

Rate at which the tank is filled =
`(1)/(15)`

In 25 hours the tap empties the tank

Rate at which the tank is drained =
`(1)/(25)`

The net gain per minute on the total filling rate is

=>
`(1)/(x) =` Rate at which the tank is filled - Rate at which the tank is drained

=>
`(1)/(x) = (1)/(15) - (1)/(25)`

=>
`(1)/(x) = (25-15)/(15 * 25)`

=>
`(1)/(x) = (10)/(375)`

=> 10x = 375

=>
`x = (375)/(10)`

=>x = 37.5