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    Question

    David can complete a work alone in 30 days, while Ethan

    can complete the same work in 50 days. Both of them started the work together and worked till 96% of the work is completed and then David left the work. If the remaining work is done by Ethan alone, then find the time taken to complete the whole work.
    A 20 days Correct Answer Incorrect Answer
    B 18 days Correct Answer Incorrect Answer
    C 28 days Correct Answer Incorrect Answer
    D 18 days Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, Let the total work = 300 units (L.C.M of 30 and 50 units) Efficiency of David = 300/30 = 10 units/day Efficiency of Ethan = 300/50 = 6 units/day 96% of the work = 0.96 × 300 = 288 units Number of days taken by David and Ethan to complete 288 units = 288/(10 + 6) = 18 days Remaining work = 300 – 288 = 12 units Number of days taken by Ethan to complete 12 units of the work = 12/6 = 2 days Total time taken to complete the work = 18 + 2 = 20 days

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