Important word problems on Linear Equations in two variables 2

Question for practice
The following questions are more helpful for class tenth students for all boards.

Questions.  4 men and 4 boys do a piece of work 3 in days, while 7 men and 2 boys finish it in 4 days. In how days 6 men and 12 boys will finish it?

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Comments

  1. Unknown18 August 2012 at 08:47

    let the number of men be x and the number of boys be y.
    then 4x+4y=3(1)
    7x+2y=4(2)
    3x-2y=1(3)
    6x-4y=2(4)
    6x+12y=z(5)
    8y=z-2
    y=z-2/8
    from (2) and (3)
    x=1/2
    6X1/2-4y=2
    3-4y=2
    -4y=-1
    y=-1/-4
    y=1/4
    1/4=z-2/8(5)
    1/4+2/8=z
    z=1/2=2
    therefore,6 men and 12 boys will finish the work in 2 days

    ReplyDelete
    Replies
    1. maths4all20 August 2012 at 03:14

      check this
      Sol Let work done by 1 man = x
      work done by 1 man in 1 day = 1/x
      Let work done by 1 boy = y
      work done by 1 boy in 1 day = 1/y
      4/x + 4/y = 1/3 .....(1)
      7/x + 2/y = 1/4 .....(2)
      Let 1/x = a
      Let 1/y = b
      4a + 4b = 1/3 .....(3)
      7a + 2b = 1/4 .....(4)
      Using elimination from (3) and (4),
      a = 1/60
      or 1/x = 1/60
      or x = 60
      b = 1/15
      or 1/y = 1/15
      or y = 15
      therefore, no of days taken by 6 men and 12 boys to do the work
      =6(1/60) +12(1/15)
      =54/60
      = 9/10
      therefore, 6 men and 12 boys take 10/9 days to do the work.

      Delete
  2. Unknown18 August 2012 at 09:33

    This comment has been removed by the author.

    ReplyDelete
  3. Unknown18 August 2012 at 09:34

    let the number of men be x
    let the number of boys be y.
    then (1) ....4x+4y=3
    (2)........7x+2y=4
    (3).........3x-2y=1
    (4).........6x-4y=2
    (5) .........6x+12y=z
    8y=z-2
    y=z-2/8
    from (2) and (3) we get ...
    x=1/2
    6X1/2-4y = 2
    3-4y = 2
    -4y = -1
    y = -1/-4
    y = 1/4
    1/4 = z-2/8(5)
    1/4+2/8 = z
    z = 1/2=2
    therefore,6 men
    12 boys

    will finish the work in 2 days

    ReplyDelete
    Replies
    1. maths4all20 August 2012 at 03:15

      check this
      Sol Let work done by 1 man = x
      work done by 1 man in 1 day = 1/x
      Let work done by 1 boy = y
      work done by 1 boy in 1 day = 1/y
      4/x + 4/y = 1/3 .....(1)
      7/x + 2/y = 1/4 .....(2)
      Let 1/x = a
      Let 1/y = b
      4a + 4b = 1/3 .....(3)
      7a + 2b = 1/4 .....(4)
      Using elimination from (3) and (4),
      a = 1/60
      or 1/x = 1/60
      or x = 60
      b = 1/15
      or 1/y = 1/15
      or y = 15
      therefore, no of days taken by 6 men and 12 boys to do the work
      =6(1/60) +12(1/15)
      =54/60
      = 9/10
      therefore, 6 men and 12 boys take 10/9 days to do the work.

      Delete
  4. Rahul Daswani18 August 2012 at 10:07

    Let the time taken by 1 man to do the work be x and the time taken by 1 boy to do the work be y.
    Let 1/x be equal to p and 1/y be equal to q.
    Let the number of days taken by 6 men and 12 boys to complete the work be A.
    Then
    4/x + 4/y = 3
    4p + 4q = 3 ....( 1 )
    And
    7/x + 2/y = 4
    7p + 2q = 4 ....( 2 )
    [ 7p + 2q = 4 ] * 2
    14p + 4q = 8 ....( 3 )
    Subtracting ( 1 ) from ( 3 )
    10p = 5
    p = 1/2

    x = 1/p
    x = 2

    Putting p = 1/2 in ( 1 )
    4[1/2] + 4q = 3
    4q = 3 - 2
    q = 1/4

    y = 1/q
    y = 4

    6/x + 12/y = A
    6p + 12q = A
    6[1/2] + 12[1/4] = A
    3 + 3 = A
    A = 6
    Thus, the number of days taken by 6 men and 12 boys to complete the work are 6 days.

    ReplyDelete
    Replies
    1. maths4all20 August 2012 at 03:04

      do it again ...

      Delete
    2. maths4all20 August 2012 at 03:15

      check this
      Sol Let work done by 1 man = x
      work done by 1 man in 1 day = 1/x
      Let work done by 1 boy = y
      work done by 1 boy in 1 day = 1/y
      4/x + 4/y = 1/3 .....(1)
      7/x + 2/y = 1/4 .....(2)
      Let 1/x = a
      Let 1/y = b
      4a + 4b = 1/3 .....(3)
      7a + 2b = 1/4 .....(4)
      Using elimination from (3) and (4),
      a = 1/60
      or 1/x = 1/60
      or x = 60
      b = 1/15
      or 1/y = 1/15
      or y = 15
      therefore, no of days taken by 6 men and 12 boys to do the work
      =6(1/60) +12(1/15)
      =54/60
      = 9/10
      therefore, 6 men and 12 boys take 10/9 days to do the work.

      Delete
  5. Mahima Batheja18 August 2012 at 23:56

    work done by a man in 1 day = 1/x
    work done by a boy in 1 day = 1/y
    4/x + 4/y = 1/3 ------ [1]
    7/x + 2/y = 1/4 -------[2]
    by elimination ...
    x = 60 ( days taken by 1 man to do a piece of work}
    y = 15 ( days taken by 1 boy to do the same piece of work}
    then days taken by 6 men and 12 boys =
    6/x + 12/y
    substituting values of x and y
    6/(60) + 12/(15)
    = 9/10
    therefore, 6 men and 12 boys take 9/10 days to complete the work.

    ReplyDelete
  6. Unknown19 August 2012 at 08:52

    Ans. Let work done by 1 man = x
    work done by 1 man in 1 day = 1/x
    Let work done by 1 boy = y
    work done by 1 boy in 1 day = 1/y
    4/x + 4/y = 1/3 .....(1)
    7/x + 2/y = 1/4 .....(2)
    Let 1/x = a
    Let 1/y = b
    4a + 4b = 1/3 .....(3)
    7a + 2b = 1/4 .....(4)
    by elimination from (3) and (4),
    a = 1/60
    or 1/x = 1/60
    or x = 60
    b = 1/15
    or 1/y = 1/15
    or y = 15
    therefore, no of days taken by 6 men and 12 boys to do the work
    =6(1/60) +12(1/15)
    =54/60
    = 9/10
    therefore, 6 men and 12 boys take 9/10 days to do the work.

    ReplyDelete

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