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    Question

    'A' requires 16 more days to finish a task compared to

    'B'. When 'A' and 'B' collaborate, they complete the task in 9 days fewer than 'B' would need to finish it on his own. Determine the number of days it takes for 'A' to complete the task alone.
    A 30 days Correct Answer Incorrect Answer
    B 48 days Correct Answer Incorrect Answer
    C 24 days Correct Answer Incorrect Answer
    D 32 days Correct Answer Incorrect Answer
    E 40 days Correct Answer Incorrect Answer

    Solution

    Let the time taken by 'B' to complete the work in 'y' days Time taken by 'A' to complete the work = (y + 16) days Time taken by them to complete the work together = (y - 9) days So, 1/y + 1/(y + 16) = 1/(y - 9)  Or, (2y + 16) X (y - 9) = y2 + 16y Or, 2y2 - 18y + 16y - 144 = y2 + 16y Or, 2y2 - 2y - 144 = y2 + 16y Or, y2 - 18y - 144 = 0 Or, y2 - 24y + 6y - 144 = 0 Or, y(y - 24) + 6(y - 24) = 0 Or, (y + 6) (y - 24) = 0 So, 'y' = 24, or 'y' = - 6 Since number of days cannot be negative, so y = 24 Therefore, time taken by 'A' alone to complete the work = 24 + 16 = 40 days

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