Question

There is a leak in the bottom of a tank. This leak can empty a full tank in 8 hours. When the tank is full, a tap is opened into the tank which admits 6 litres per hour and the tank is now emptied in 12 hours. What is the capacity of the tank?

• A. 28.8 litres
• B. 36 litres
• C. 144 litres
• D. Can't be determined

Answer 1

The correct option is C 144 litres

Let the capacity of tank be x litres
In one hour tank empties $=\frac{1}{8}\times x=\frac{x}{8}litre$
In one hour, tap admits 6 litres
After opening tap, tank is emptied in 12 hours.
So in one hour tank empties by $\frac{1}{12}\times x=\frac{x}{12}litres.$
Therefore equation becomes $6-\frac{x}{8}=-\frac{x}{12}$
$6=\frac{x}{8}-\frac{x}{12}=\frac{x}{24}$
$\therefore x=144litres$