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    Question

    If 'A' needs 24 more days to complete a certain task

    working alone compared to when 'A' and 'B' work together, and 'A' is 50% more efficient than 'B', what is the amount of time 'B' takes to finish the same task on their own?
    A 95 days Correct Answer Incorrect Answer
    B 20 days Correct Answer Incorrect Answer
    C 30 days Correct Answer Incorrect Answer
    D 90 days Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the time taken by 'A' to finish the work alone be '2x' days. Ratio of efficiencies of 'A' and 'B' = 3:2 Since, the work done is same, ratio of efficiencies of 'A' and 'B' will be inverse of the ratio of time taken by 'A' and 'B' to finish the work. So, time taken by 'B' to finish the work alone = 2x × (3/2) = '3x' days So, time taken by 'A' and 'B' to finish the work together = (2x - 24) days ATQ: (1/2x - 24) = (1/3x) + (1/2x) or, (1/2(x - 12)) = (2x + 3x)/(2x × 3x) or, 3x = 5 × (x - 12) or, 3x = 5x - 60 or, 2x = 60 x = 30 So, time taken by 'B' to finish the work alone = 3x = (30 × 3) = 90 days

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