Question

A leak in the bottom of a tank can empty it in $6$ hours. A pipe fills the tank at the rate of $4$ liters per minute. When the tank is full, the inlet is opened but leak emptied the tank in $8$ hours. What is the capacity of the tank?

• A. $5260$ L
• B. $5670$ L
• C. $5946$ L
• D. $5760$ L

Answer 1

The correct option is D $5760$ L

Part emptied by the leak in 1 hr$=\frac{1}{6}$

Net part emptied by the leak and the inlet pipe in 1 hr$=\frac{1}{8}$

Part fill by the inlet pipe in 1 hr$=\frac{1}{6}-\frac{1}{8}=\frac{1}{24}$

i.e inlet pipe fills the tank in 24 hr$=24\times 60=1440min.$

According to the question inlet pipe fills water at the rate of $4$ liters per minute.

Hence, water fills in $1440$ min$=1440\times 4=5760L$