Math

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There is a ratio of number of boys to girls 3:5. After adding 5 boys and 3 girls, the ratio become 5:7. How many girls were there at first?

  • Math -

    b = numbers of boys

    g = numbers of girls


    Ratio of boys to girls:

    b / g = 3 / 5 Multiply both sides by 5

    5 b / g = 3 Multiply both sides by g

    5 b = 3 g Divide both sides by 5

    b = 3 g / 5


    After adding ratio is :

    ( b + 5 ) / ( g + 3 ) = 5 / 7

    [ ( 3 g / 5 ) + 5 ] / ( g + 3 ) = 5 / 7 Multiply both sides by 7

    7 [ ( 3 g / 5 ) + 5 ] / ( g + 3 ) = 5 Multiply both sides by ( g + 3 )

    7 [ ( 3 g / 5 ) + 5 ] = 5 ( g + 3 )

    7 * 3 g / 5 + 7 * 5 = 5 ( g + 3 )
    21 g / 5 + 35 = 5 ( g + 3 ) Multiply both sides by 5

    21 g + 35 * 5 = 5 * 5 ( g + 3 )

    21 g + 175 = 25 ( g + 3 )

    21 g + 175 = 25 g + 25 * 3

    21 g + 175 = 25 g + 75

    175 - 75 = 25 g - 21 g

    100 = 4 g

    4 g = 100 Divide both sides by 4

    g = 100 / 4

    g = 25



    b = 3 g / 5

    b = 3 * 25 / 5

    b = 75 / 5

    b = 15


    Checking :

    b / g = 15 / 25 =

    ( 5 * 3 ) / ( 5 * 5 ) = 3 / 5


    ( b + 5 ) / ( g + 3 ) =

    ( 15 + 5 ) / ( 25 + 3 ) =

    20 / 28 =

    ( 4 * 5 ) / ( 4 * 7 ) = 5 / 7

  • Math -

    Initial:

    number of boys to girls 3:5
    =3U:5U

    U means unit
    Later (3U +5): (5U +3) = 5:7

    3U+5 5
    ----- = ---
    5U+3 7

    Cross multiply

    21U+35 = 25U+15
    35-15 = 25U-21U
    20 = 4U
    Therefore 1U =5

    Initially girls are 5Units.
    So the answer is 25.

  • Math -

    My answer is also numbers of girls

    g = 25

  • Math -

    Thanks a lot Bosnian.
    Answer is exactly correct. Just wanted to provide the alternate method which got through Maths olympiad book.

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