Question

    Worker A can build a wall alone in 30 days. When A and B

    work together, they can complete the wall in 16 days. If B starts building the wall alone and works for 20 days before leaving, how many additional days will A need to finish the remaining work alone?
    A 10 days Correct Answer Incorrect Answer
    B 11 days Correct Answer Incorrect Answer
    C 12.5 days Correct Answer Incorrect Answer
    D 14.5 days Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the total work to be done to build the wall = L.C.M of 30 and 16 = 240 units
    Then, efficiency of ‘A’ = 240 ÷ 30 = 8 units/day
    Combined efficiency of ‘A’ and ‘B’ = 240 ÷ 16 = 15 units/day
    So, efficiency of ‘B’ = 15 – 8 = 7 units/day
    Work done by ‘B’ in 20 days = 7 × 20 = 140 units
    Remaining work = 240 – 140 = 100 units
    Time taken by ‘A’ to complete the remaining work = 100 ÷ 8 = 12.5 days

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