Q7
ArithmeticTime & Work, Pipes & Cisterns
A pipe can fill a tank with water in 3 hours. Due to leakage in bottom, it takes $3\frac{1}{2}$ hours to fill it. In what time the leak will empty the fully filled tank?
- a.12 hours
- b.21 hours
- c.$6\frac{1}{2}$ hours
- d.$10\frac{1}{2}$ hours
Answer: (B) 21 hours
The pipe fills $\frac{1}{3}$ of the tank per hour, while pipe and leak together fill $\frac{2}{7}$ per hour. The leak therefore empties $\frac{1}{3} - \frac{2}{7} = \frac{1}{21}$ per hour, i.e. the full tank in 21 hours. 12 or $10\frac{1}{2}$ hours would make the leak too strong to allow filling in $3\frac{1}{2}$ hours.