Posted by **Surya** on Saturday, February 11, 2012 at 1:05am.

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 -
**Bosnian**, Saturday, February 11, 2012 at 5:30am
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 -
**Surya**, Wednesday, February 15, 2012 at 12:15pm
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 -
**Bosnian**, Wednesday, February 15, 2012 at 3:52pm
My answer is also numbers of girls

g = 25

- Math -
**Surya**, Thursday, March 8, 2012 at 9:30am
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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