Question
‘P’ can complete 80% of a task in 32 days and
‘Q’ can do 60% of the task in 54 days. If ‘P’, ‘Q’, and ‘R’ all work together, they can complete the full task in 24 days. What is the ratio of the efficiencies of ‘P’, ‘Q’, and ‘R’?Solution
ATQ,
Time taken by P to complete the work = (32/80) × 100 = 40 days Time taken by Q to complete the work = (54/60) × 100 = 90 days Time taken by P, Q and R together = 24 days Let total work = 360 units Work done by P in one day = 360 / 40 = 9 units Work done by Q in one day = 360 / 90 = 4 units Work done by all three in one day = 360 / 24 = 15 units Work done by R alone = 15 – 9 – 4 = 2 units Required ratio = 9 : 4 : 2
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