Question

A leak in the bottom of a tank can empty the full tank in 6 hours. an inlet pipe fills water at the rate of 4 liters a minute. when the tank is full, the inlet is opened and due to the leak, the tank is empty in 24 hours. how many liters does the cistern hold?

Answer 1

pipe taken time to fill 4litres =1min.
pipe taken time to fill full tank=24hr.
24hr=24*60min
       =1440min.
Volume of water in tank=4litres*1440min
                                     =5760litres.Ans.
I hope it may help u.

Answer 2

The volume of the tank is 1920 liters.

Step-by-step explanation:

The volume of the tank is assumed to be V liters.

So, the tank becomes empty after 6 hours through the leak.

Then, the rate of leaking is $\frac{V}{6 \times 60} = \frac{V}{360}$ liters per minute.

Now, the tank is filled up at the rate of 4 liters per minute.

So, the resultant rate of emptying the tank is ($(\frac{V}{360} - 4) = \frac{V - 1440}{360}$ liters per minute.

Now, it takes 24 hours i.e. (24 × 60) = 1440 minutes to empty the tank.

So, we can write the equation as $\frac{V - 1440}{360} \times 1440 = V$

⇒ V - 1440 = 0.25V

⇒ 0.75V = 1440

⇒ V = 1920 liters.

Therefore, the volume of the tank is 1920 liters. (Answer)