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    Question

    A, B, and C can together complete a task in 12 days. A

    and B can complete the same task in 16 days, and B and C can complete it in 20 days. In how many days will A, B, and C together complete the task if A works alone for the first 5 days?
    A 8 days Correct Answer Incorrect Answer
    B 10 days Correct Answer Incorrect Answer
    C 12 days Correct Answer Incorrect Answer
    D 14 days Correct Answer Incorrect Answer

    Solution

    Let the total work be W. From the given data: 1/A + 1/B + 1/C = 1/12, 1/A + 1/B = 1/16, 1/B + 1/C = 1/20. Solving these, we find: 1/A = 1/30, 1/C = 1/48, and 1/B = 7/240. Now, A works alone for the first 5 days, so work done = 5 * 1/30 = 1/6. Remaining work = W – 1/6 = 5/6. Now, A, B, and C work together, so time taken = 5/6 / (1/12) = 10 days Correct Option: b)

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