A cistern can be filled separately by two pipes P and Q in 45 min and 35 min respectively. A tap R at the bottom can empty the full cistern in 30 min. If the tap R is opened 7 min after the two pipes P and Q are opened then after what time from the opening of pipe
rate of P = 1/45
rate of Q = 1/35
rate of R = -1/30
combined rate of P and Q = 1/45 + 1/35 = 16/315
part of cistern filled after 7 minutes = 7(16/315) = 16/45
At this point your question is incomplete.
Where does tap R enter the picture ?
Are all taps turned on at the same time?
Who knows ?
you decide and finish the problem.