Question
A task can be finished by 'P' and 'Q' alone in 10 days
and 5 days, respectively. 'P' and 'Q' started the task together and after 3 days, 'P' was replaced by 'R'. If the entire task was completed in (20/3) days, find how many days 'R' alone would take to complete the task.Solution
ATQ,
Let the efficiency of 'R' be 'x' units/day Let total work = 30 units (LCM of 10 and 5) Efficiency of 'P' = 30/10 = 3 units/day Efficiency of 'Q' = 30/5 = 6 units/day According to the question: (3 + 6) × 3 + (6 + x) × {(20/3) − 3} = 30 Or, (11/3) × (6 + x) = 30 − 27 Or, 6 + x = 9 Or, x = 3 Number of days required by 'R' to finish the work alone = 30/3 = 10 days
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