Question : A pipe can fill a tank in 24 hours. Due to a leakage at the bottom, it is filled in 36 hours. If the tank is half full, how much time will the leak take to empty the tank?
Option 1: 48 hours
Option 2: 72 hours
Option 3: 36 hours
Option 4: 24 hours
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Correct Answer: 36 hours
Solution :
Given: A pipe can fill a tank in 24 hours.
Let the total work = LCM of 24 and 36 = 72 units
One hour work of filling pipe = 72 $\div$ 24 = 3 units
One hour of work filling pipe and the leakage = 72 $\div$ 36 = 2 units
One hour work of the leakage = 3 – 2 = 1 unit
Half capacity of the tank = half of 72 units = 36 units
So, the required time by the leak = $\frac{36}{1}$ = 36 hours
Hence, the correct answer is 36 hours.
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