Question

A leak in the bottom of a reservoir can empty the full reservoir in 12 hours. An inlet canal fills water at the rate of 8 litres a minute. When the reservoir is full the inlet is opened and due to the leak the reservoir is empty in 16 hours. The capacity of the reservoir in litres is:

• A. 14280 litres
• B. 5760 litres
• C. 31440 litres
• D. 11520 litres
• E. 23040 litres

Answer 1

The correct option is E

23040 litres

Time taken to empty the reservoir with leak = $\frac{1}{12}$ hour

Time taken to empty the reservoir with leak and inlet = $\frac{1}{16}$ hour

Work done by the inlet in 1 hour= ($\frac{1}{12}$ - $\frac{1}{16}$) =$\frac{16-12}{12\times 16}=\frac{1}{48}$

For 1 minute = $\frac{1}{48}$ $\times$ $\frac{1}{60}$=$\frac{1}{2880}$

An inlet canal fill water at the rate of 8 litres a minute = 2880 $\times$ 8 = 23040 litres