Question
‘P’ can complete a project in 12 days. ‘Q’ is
40% less efficient than ‘P’. Working together, ‘P’, ‘Q’ and ‘R’ can finish the job in 5 days. In how many days will ‘R’ finish the job working alone?Solution
ATQ,
Time taken by ‘P’ to complete the whole work alone = 12 days Time taken by ‘Q’ to complete the whole work alone = 12 / 0.6 = 20 days Let the total work = 60 units (L.C.M of 12 and 20) Efficiency of ‘P’ = 60 / 12 = 5 units/day Efficiency of ‘Q’ = 60 / 20 = 3 units/day Let the efficiency of ‘R’ be x units/day According to the question, (5 + 3 + x) × 5 = 60 Or, 5x = 60 – 25 – 15 Or, x = 20 / 5 = 4 units/day Time taken by ‘R’ to complete the whole work alone = 60 / 4 = 15 days
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