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Discussion :: Time and Work

  1. A can finish the job at the same time in which B and C together do it. If A and B together can finish the work in 10 days and C alone can do the work in 50 days, how many days B will take to complete the same job?
    2. A.
    20 days
    B.
    22 days
    C.
    22(1/2) days
    D.
    25 days

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    Answer : Option D

    Explanation :

    ATQ,

    The efficiency of A = B+C
    (A+B) can finish the work in 10 days, and C can finish the work in 50 days.

    Now, A+B = 10 days
    C = 50 days

    Note: Assume the total work = LCM of the given days

    Take the LCM of days = LCM of (10 and 50) = 50
    Let the total work = 50

    Note: One day work = (total work/ days)

    Now,

    C's one day work = 50/50 = 1
    (A+B)'s one day work = 5

    i.e., (A+B+C)'s one day work = 5+1=6

    i.e., A+A = 6
    Or, A's one day work efficiency = 3

    A+B = 5, i.e., 3+B = 5
    Or, B's one day efficiency=2
    Hence, B alone can work in 50/2 = 25 days

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