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    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?
    A (20/3) days Correct Answer Incorrect Answer
    B (10/3) days Correct Answer Incorrect Answer
    C (40/3) days Correct Answer Incorrect Answer
    D (29/3) days Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    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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