A leak in the bottom of a tank can empty the full tank in $8$ hours. An inlet pipe fills water at the rate of $6$ liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in $12$ hours. How many liters does the cistern hold ?

A) 7980

B) 7860

C) 8640

D) 8340


Option C


Work done by the inlet in $1$ hour $=\left(\frac{1}{8}-\frac{1}{12}\right)$ $=\frac{1}{24}$.

Work done by the inlet in $1$ min. $=\left(\frac{1}{24}\times\frac{1}{60}\right)$ $=\frac{1}{1440}$.

$\therefore$ Volume of $\frac{1}{1440}$ part $= 6$ liters.

$\therefore$ Volume of whole $=(1440\times 6)$ liters = 8640 liters