Mathematics2 men and 7 boys can do a piece of work in 4 days. The same work is done in 3 days by 4 men and 4 boys. How long respectively would it take for one man and one boy to do it?

2 men and 7 boys can do a piece of work in 4 days. The same work is done in 3 days by 4 men and 4 boys. How long respectively would it take for one man and one boy to do it?


  1. A
    15 days, 60 days
  2. B
    20 days, 40 days
  3. C
    10 days, 30 days
  4. D
    90 days, 40 days 

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    Solution:

    Given that 2 men and 7 boys can do a piece of work in 4 days and the same work is done by 4 men and 4 boys in 3 days.
    Let's suppose that one man alone can finish the work in x days and one boy alone finish it in y days.
    Thus, one man's one day's work is 1x.
    And one boy's one day's work is 1y.
    Also, 2 men’s one day's work is 2x and 7 boy’s one day's work is 7y.
    According to the question,
    2x+7y=14
    8x+28y-1=0   ...(1)
    Again, from the question, writing the algebraic representation of the second condition,
    4x+4y=13
    12x+12y-1=0   ... (2)
    Substituting 1x for u and 1y for v in equation (1) and (2),
    8u+28v-1=0
    12u+12v-1=0
    The solution of the equations a1u+b1v+c1=0 and a2u+b2v+c1=0 by cross multiplication method is given by the formula,
    ub1c2-b2c1=va2c1-a1c2=1a1b2-a2b1
    Here, a1=8,b1=28, c1=-1, a2=12,b2=12, c2=-1.
    Using the cross-multiplication method to find the value of u and v,
    u28-1-12-1=v12-1-8-1=1812-2812
    u-28+12=v-12+8=196-326
    u-16=v-4=1-240
    u=-16-240=115
    v=-4-240=160
    Again, substituting 1x for u and 1y for v, to find the value of x and y.
    115=1x
     x=15
    160=1y
    y=60
    Therefore, we can say that, 1 man takes 15 days to complete the work and 1 boy takes 60 days to complete the same work.
    Hence, option (1) is correct.
     
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