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    Question

    "A" and "B" collaborate to complete a project in 18

    days. If "A" can finish the project 15 days faster than "B" when working solo, how long would it take "B" to complete the project alone?
    A 45 days Correct Answer Incorrect Answer
    B 6 days Correct Answer Incorrect Answer
    C 30 days Correct Answer Incorrect Answer
    D 60 days Correct Answer Incorrect Answer

    Solution

    Let the time taken by 'B' to finish the work be 'x' days. So, time taken by 'A' to finish the work = 'x - 15' days ATQ; (1/18) = (1/x) + {1/(x - 15) } Or, (1/18) X (x - 15) X x = (x - 15) + x Or, x2 - 15x = 18 X (2x - 15) Or, x2 - 15x = 36x - 270 Or, x2 - 51x + 270 = 0 Or, x2 - 45x - 6x + 270 = 0 Or, x(x - 45) - 6(x - 45) = 0 Or, (x - 45) (x - 6) = 0 So, x = 45 or x = 6 Since, at x = 6, time taken by 'A' to finish the work would become negative So, x = 45 So, 'B' would finish the work alone in 45 days. Hence, option a.

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