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    Question

    A contractor assigned a job to three persons A, B and C.

    ‘A’ which is 25% less efficient than ‘B’ can complete 20% of a work in 8 days. ‘C’ takes 10 days more than ‘B’ to complete the same work. ‘A’ and ‘B’ started working together and after 4 days C joined them. Due to some personal emergency ‘A’ left after 5 more days and rest of the work is completed by 'B' and 'C', together. Find the total time taken to complete the whole work.
    A 11 days Correct Answer Incorrect Answer
    B 18 days Correct Answer Incorrect Answer
    C 15 days Correct Answer Incorrect Answer
    D 10 days Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Time taken by ‘A’ to complete the work alone = 8/0.2 = 40 days Time taken by ‘B’ to complete the work alone = 0.75 × 40 = 30 days Time taken by ‘C’ to complete the work alone = 30 + 10 = 40 days Let, the total work = 120 units Efficiency of ‘A’ = 120/40 = 3 units/day Efficiency of ‘B’ = 120/30 = 4 units/day Efficiency of ‘C’ = 120/40 = 3 units/day Work completed in 4 days = 4 × (3 + 4) = 28 units Work completed in next 5 days = 5 × (3 + 4 + 3) = 50 units Time taken by ‘B’ and ‘C’ to complete remaining work together = (120 – 78)/7 = 6 days Therefore, total time taken = 4 + 5 + 6 = 15 days

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