Question
Ajay and Vijay can finish a task in 9 days working
together. Charu, who is twice as efficient as Vijay, can complete the task alone in 18 days. If Ajay and Vijay begin the work, and Charu joins them after 4 days, in how many total days will the entire work be completed?Solution
ATQ,
Let the Ajay, Vijay and Charu can be define as A, B and C respectively.
Let total amount of work be 18 units {LCM of (9 and 18)}
Efficiency of ‘A’ and ‘B’ together = (18/9) = 2 units/day
Efficiency of ‘C’ alone = (18/18) = 1 units/day
Given, Efficiency of ‘C’ = 2 × efficiency of ‘B’
So, efficiency of ‘B’ = 0.5 units/day
So, efficiency of ‘A’ = (2 – 0.5) = 1.5 units/day
Work done by ‘A’ and ‘C’ together in 4 days = 4 × (1.5 + 1) = 10 units
Remaining work = 18 – 10 = 8 units
So, 8 units of work will be completed by ‘A’, ‘B’ and ‘C’ together in = {8/(1.5 + 0.5 + 1)} = (8/3) days
Therefore, total time taken to complete the work = 4 + (8/3) = (20/3) days
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