From a group of boys and girls, 14 girls
leave first. Then the ratio of the number of girls to the number of boys
becomes 1:2. After this, 43 boys leave the group. Now the boys and
girls are equal in number. How many girls were there in the beginning?
let the number of girls = x
and number of boys = y
According to question ,
After 14 girls left the group ,
x - 14 /y = 1/2
or 2( x - 14 ) = y
2x - 28 = y ................. (1st )
After 43 boys left the group ,
x-14/y - 43 =1
x - 14 = y - 43
x - 14 + 43 = y
x +29 = y .......................... (2nd )
Using 2nd in 1st , we get
2x - 28 = x +29
2x = x+29 +28
2x - x = 29 + 28
x = 57
Hence the number of girls in the beginning were 57.
Hope this helps You!!