in How Many Days can A Alone do it? If

A and B can do a piece of work in 72 days. B and C can do it in 120 days. A and C can do it in 90 days. In what time can A alone do it?

  1. 80 days
  2. 100 days
  3. 120 days
  4. 150 days
vijay Professor Asked on 5th August 2015 in Maths.
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  • 1 Answer(s)

    Answer: (3) 120 days
    Explanation:-
    A and B can do a piece of work = 72 days
    Therefore, A  and B  can do a piece of work in a day = 1/72.

    B and C can do it = 120 days
    Therefore, B and C can it in a day = 1/120

    A and C can do it = 90 days
    Therefore, A and C can do in a day = 1/90

    Then, A , B  & C can do it in a day = (1/72 + 1/120 + 1/90 ) / 2
    = (5 + 3 + 4)/360 x 2
    = 12 /360 x 2
    = 1/30 x 2
    = 1/60

    Then, A alone can do it in a day  = 1/60 – 1/120
    = (2 – 1 ) /120
    = 1/120
    Therefore, A alone can do complete the work = 120 days.

    Hence, the answer is (3) 120 days.

    Anurag Mishra Professor Answered on 6th August 2015.
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