Question
Together, the three intake pipes, "P," "Q," and "R," can
fill a water tank in eight hours. While the three pipes are opened simultaneously, pipe "Q" closes after three hours. Determine how long pipe "Q" took to fill the same tank by itself if pipes "P" and "R" completed the remaining portion in 9 hours.Solution
ATQ, Let quantity filled by pipe βPβ, βQβ and βRβ together in 8 hrs = 1 litres Quantity filled by pipe βPβ, βQβ and βRβ together in 1 hrs = (1/8) litres Quantity filled by pipe βPβ, βQβ and βRβ together in 3 hrs = (3/8) litres Remaining quantity to be filled = {1 β (3/8)} = (5/8) litres Quantity filled by pipe βPβ and βRβ together in 9 hrs = (5/8) litres Quantity filled by pipe βPβ and βRβ together in 1 hrs = (5/72) litres Quantity filled by pipe βQβ alone in 1 hour = (1/8) β (5/72) = (4/72) litres So, pipe βQβ alone can fill the tank in (72/4) = 18 hrs
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