A tank has a leak which would empty the tank in 16 hours. If the tank is full of water and a tap is turned on which admits 4 liters a minute into the tank, and it is now emptied in 48 hours. How many liters does the tank hold?
Solution
Correct Answer: Option A
Let the capacity of the tank be x litres,
According to the given information,
Quantity of water emptied by the leak in 1 hour = (x/16) litres
Quantity of water filled by the tap in 1 hour = 4 × 60 = 240 litres
When both the taps are turned on, quantity of water emptied by the tank in one hour = (x/48) litres
According to the Question,
\(\begin{array}{l} \frac{x}{{16}}\; - 240 = \;\frac{x}{{48}}\\ \Rightarrow \;\frac{{3x - x}}{{48}} = 240\\ \Rightarrow x = \frac{{240 \times 48}}{2} \end{array}\)
⇒ x = 5760 litres
Hence, the tank holds 5760 liters of water.
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