Question
‘P’ and ‘Q’ can complete a task in 72 days,
while ‘Q’ and ‘R’ can finish 60% of the same task in 27 days. If ‘R’ is twice as efficient as ‘P’, how many days will ‘R’ alone take to complete the entire task?Solution
Time taken by ‘Q’ and ‘R’ to do the whole work = (27 × 100) / 60 = 45 days Let total work = LCM of 72 and 45 = 360 units Efficiency of ‘P’ and ‘Q’ = 360 / 72 = 5 units/day Efficiency of ‘Q’ and ‘R’ = 360 / 45 = 8 units/day Let efficiency of ‘P’ = y Then efficiency of ‘R’ = 2y ATQ, (Q + R) - (P + Q) = 2y - y = y = 3 ⇒ y = 3 ⇒ R’s efficiency = 2 × 3 = 6 units/day Time taken by ‘R’ = 360 / 6 = 60 days
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