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?

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