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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?

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,
$$\eqalign{ & \Rightarrow \frac{{\text{q}}}{{10}} - \frac{{\text{q}}}{{15}} = 240 \cr & \Rightarrow \frac{{3{\text{q}} - 2{\text{q}}}}{{30}} = 240 \cr & \Rightarrow \frac{9}{{30}} = 240 \cr & \Rightarrow {\text{q}} = 240 \times 30 \cr & \Rightarrow {\text{q}} = 7200\,{\text{litres}} \cr} $$

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