Question

A leak in the bottom of a container can empty the full tank in 4 hours. An inlet pipe fills water at the rate of 3 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 6 hours. How many litres does the container hold?

• A. 3600 litres
• B. 2880 litres
• C. 2160 litres
• D. 1440 litres
• E. 1800 litres

Answer 1

The correct option is C

2160 litres

Time taken to empty the tank due to the leak is $\frac{1}{4}$

Time taken to empty the tank with the inlet+leak is $\frac{1}{6}$

Work done by the inlet in 1 hour = $\left(\frac{1}{4}-\frac{1}{6}\right)$ = $\frac{1}{12}$

Work done by the inlet in 1 minute = $\frac{1}{12}$ $\times$ $\frac{1}{60}$ = $\frac{1}{720}$

Therefore volume = 720 $\times$ 3 litres = 2160 litres