A and B together can complete some work in 24 days. If A, B and C work together, they can complete the same work in 18 days. B and C both have the same efficiency.
Q. A, B and C start working together from the very first day. If C leaves after 6 days and D (whose efficiency is equal to A) joins the work at that instant, then approximately how many days will be required to complete the work?
    Correct answer is '16'. Can you explain this answer?

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    NISTHA DHOLAKIA
    Jan 31, 2020
    We know that, A, B and C require 36, 72 and 72 days respectively to complete the work when working alone.




    From the solution to the previous question, total work = 72 units and the efficiency of A, B and C (in units/day) is 2, 1 and 1 respectively.
    Since the efficiency of D is the same as that of A, d = 2 units/day as well.
    A, B and C work together for the first 6 days.
    So, amount of work done in the first 6 days = 6(a + b + c) = 6(2 + 1 + 1) = 24 units.
    Now, C leaves and D joins the work.
    So, the remaining 48 units of work is done by A, B and D.
    Let the number of days taken by these three people by x.
    So, 48 = (2 + 1 + 2) * x
    x = 48/5 = 9.6 days
    Since the work is incomplete at the end of day 9, the number of days taken has to be considered as 10.
    So, total time taken to complete the work = 6 + 10 =16
    Answer: 16

    We know that, A, B and C require 36, 72 and 72 days respectively to complete the work when working alone.From the solution to the previous question, total work = 72 units and the efficiency of A, B and C (in units/day) is 2, 1 and 1 respectively.Since the efficiency of D is the same as that of A, d = 2 units/day as well.A, B and C work together for the first 6 days.So, amount of work done in the first 6 days = 6(a + b + c) = 6(2 + 1 + 1) = 24 units.Now, C leaves and D joins the work.So, the remaining 48 units of work is done by A, B and D.Let the number of days taken by these three people by x.So, 48 = (2 + 1 + 2) * xx = 48/5 = 9.6 daysSince the work is incomplete at the end of day 9, the number of days taken has to be considered as 10.So, total time taken to complete the work = 6 + 10 =16Answer: 16
    We know that, A, B and C require 36, 72 and 72 days respectively to complete the work when working alone.From the solution to the previous question, total work = 72 units and the efficiency of A, B and C (in units/day) is 2, 1 and 1 respectively.Since the efficiency of D is the same as that of A, d = 2 units/day as well.A, B and C work together for the first 6 days.So, amount of work done in the first 6 days = 6(a + b + c) = 6(2 + 1 + 1) = 24 units.Now, C leaves and D joins the work.So, the remaining 48 units of work is done by A, B and D.Let the number of days taken by these three people by x.So, 48 = (2 + 1 + 2) * xx = 48/5 = 9.6 daysSince the work is incomplete at the end of day 9, the number of days taken has to be considered as 10.So, total time taken to complete the work = 6 + 10 =16Answer: 16