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

Answer:

It take 37.5 hours to fill the tank

Step-by-step 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  = $\frac{1}{15}$

In 25 hours the tap empties the tank

Rate at which the tank is drained = $\frac{1}{25}$

The net gain per minute on the total filling rate  is

=> $\frac{1}{x} =$ Rate at which the tank is filled - Rate at which the tank is drained

=>$\frac{1}{x} = \frac{1}{15} - \frac{1}{25}$

=>$\frac{1}{x} = \frac{25-15}{15 \times 25}$

=>$\frac{1}{x} = \frac{10}{375}$

=> 10x  = 375

=>$x = \frac{375}{10}$

=>x = 37.5