A cistern is provided with two pipes A and B. A can fill it in 20 minutes and B can empty it in 30 minutes. If A and B be kept open alternately for one minute each, how soon will the cistern be filled?
A cistern is provided with two pipes A and B. A can fill it in 20 minutes and B can empty it in 30 minutes. If A and B be kept open alternately for one minute each, how soon will the cistern be filled?
[A]110 minutes
[B]115 minutes
[C]120 minutes
[D]121 minutes
115 minutes
Part of the tank filled in first two minutes $latex = \frac{1}{20}-\frac{1}{30} = \frac{3-2}{60} = \frac{1}{60}&s=1$
∴ Part of tank filled in 114 minutes $latex = \frac{57}{60} = \frac{19}{20}&s=1$
∴ Remaining part of cistern will be filled in 115th minute.
Hence option [B] is correct answer.