Q195
ArithmeticTime & Work, Pipes & Cisterns
Two pipes, P and Q can fill a cistern in 12 and 15 minutes respectively. If both are opened together and at the end of 3 minutes, the first is closed, how much longer will the cistern take to fill?
- a.$8\frac{3}{4}$ minutes
- b.5 minutes
- c.$8\frac{1}{2}$ minutes
- d.$8\frac{1}{4}$ minutes
Answer: (D) $8\frac{1}{4}$ minutes
In 3 minutes both pipes fill $3 \times (\frac{1}{12} + \frac{1}{15}) = \frac{9}{20}$ of the cistern. Q alone fills the remaining $\frac{11}{20}$ in $\frac{11}{20} \times 15 = 8\frac{1}{4}$ minutes. The other fractions come from slips in this arithmetic.