Q. A tank can be filled by pipe A and pipe B in 2 hours and in 6 hours respectively. At 10 AM pipe A was opened. If pipe B is opened at 11 AM then at what time the tank will be filled?
Answer: 11:45 AM
Notes: As per the question, part of the tank filled in 1 hour by pipe A $latex = \frac{1}{2}&s=1$
and by pipe B $latex = \frac{1}{3}&s=1$
then, part of the tank filled by both pipes in 1 hour $latex = \frac{1}{2}+\frac{1}{6} = \frac{3+1}{6} = \frac{2}{3}&s=1$
So, Time taken by both pipes to fill $latex \frac{2}{3}&s=1$ part of the tank = 60 minutes
∴ Time taken to fill $latex \frac{1}{2}&s=1$ part $latex = \frac{60\times 3}{2}\times \frac{1}{2} = 45 minutes&s=1$
∴ We can say that tank will be filled at 11:45 AM.
Hence option [A] is correct answer.
