Q150
ArithmeticTime & Work, Pipes & Cisterns
Two pipes can fill a cistern in 20 minutes and 30 minutes respectively. Both pipes being opened, time when the first pipe must be turned off so that the cistern may be filled in 10 minutes more will be
- a.8 minutes
- b.9 minutes
- c.10 minutes
- d.12 minutes
Answer: (A) 8 minutes
The second pipe works throughout, and after the first is closed it needs 10 more minutes, in which it fills $\tfrac{10}{30} = \tfrac{1}{3}$ of the cistern. So the two pipes together must fill $\tfrac{2}{3}$ before that; their joint rate is $\tfrac{1}{20}+\tfrac{1}{30} = \tfrac{1}{12}$ per minute, which takes $\tfrac{2}{3}\times12 = 8$ minutes. So the first pipe is turned off after 8 minutes (total time 18 minutes).