In how many days will finish the job?

3 men and 6 women finish a job in 9 days while 2 men and 8 women finish it in 12 days. In how many days will 12 women working alone will finish the same job?

  1. 36 days
  2. 30 days
  3. 32 days
  4. 34 days
Anurag Mishra Professor Asked on 7th January 2016 in Maths.
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  • 1 Answer(s)

    Answer: (1) 36 days

    Explanation:-
    Let 1 man’s 1 day’s work be X and 1 woman’s 1 day’s work be Y,

    3 men and 6 women finish a job in 9 days.
    Then, 3 X + 6 Y = 1/9  ……………………(1)
    And  2 X + 8 Y = 1/12            ……………(2)

    Equation (1) multiply by 2  and equation (2)  multiply 3,
    6 X + 12 Y = 2/9    ………………………… (3)
    6 X + 24 Y = 3/12 …………………………(4)

    Equation (3) subtracted from equation (4),
    6 X + 24 Y – 6 X – 12 Y = 3/12 – 2/9
    12 Y = 1/36
    Y = 1/36 x 12
    = 1/432

    Then, 1 woman’s 1 day’s work = 1/432
    Therefore, 12 women’s  work = 12/432
    = 1/36

    Then, In 36 days, 12 women will be working alone finish the same job.

    Hence, the correct answer is option (1) 36 days.

    Anurag Mishra Professor Answered on 9th January 2016.
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