A pump can fill a milk tank in 2 hours. Because of a leakage problem it took 20 minutes more to fill the tank. The plant supervisor wants to find that how much time would the leak take to empty a full tank
a) 4 1/3 hours b) 7 hours c) 8 hours d) 14 hours
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let the capacity of tank be C litres.
Filling rate of the pump when there is no leak = C / 2 litres/hour
Filling rate of the pump + leak together = C / [ 2 + 1/3 ] = C /(7/3) = 3C/7 litres/hr
Emptying rate of leak = C/2 - 3C/7 = C/14
Then leak can empty tank in capacity / leak rate = C / [ C/14 ] = 14 hours
Filling rate of the pump when there is no leak = C / 2 litres/hour
Filling rate of the pump + leak together = C / [ 2 + 1/3 ] = C /(7/3) = 3C/7 litres/hr
Emptying rate of leak = C/2 - 3C/7 = C/14
Then leak can empty tank in capacity / leak rate = C / [ C/14 ] = 14 hours
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