A tank has a leak which would empty the completely filled tank in 10 hours. If the tank is full of water and a tap is opened which admits 4 litres of water per minutes in the tank, the leak takes 15 hours to empty the tank. how many litres does the tank hold?
Correct Answer: 7200 litres
Let the capacity of the tank = q litres
According to the question,
Quantity of water emptied by the leak in 1 hour = $$\frac{\text{q}}{10}$$ litres
Qunatity of water filled by the tap in 1 hour = 240 litres
According to the question,
$$\eqalign{ & \Rightarrow \frac{{\text{q}}}{{10}} - \frac{{\text{q}}}{{15}} = 240 \cr & \Rightarrow \frac{{3{\text{q}} - 2{\text{q}}}}{{30}} = 240 \cr & \Rightarrow \frac{9}{{30}} = 240 \cr & \Rightarrow {\text{q}} = 240 \times 30 \cr & \Rightarrow {\text{q}} = 7200\,{\text{litres}} \cr} $$
According to the question,
Quantity of water emptied by the leak in 1 hour = $$\frac{\text{q}}{10}$$ litres
Qunatity of water filled by the tap in 1 hour = 240 litres
According to the question,
$$\eqalign{ & \Rightarrow \frac{{\text{q}}}{{10}} - \frac{{\text{q}}}{{15}} = 240 \cr & \Rightarrow \frac{{3{\text{q}} - 2{\text{q}}}}{{30}} = 240 \cr & \Rightarrow \frac{9}{{30}} = 240 \cr & \Rightarrow {\text{q}} = 240 \times 30 \cr & \Rightarrow {\text{q}} = 7200\,{\text{litres}} \cr} $$