At the beginning of the year, the ratio of boys to girls in high school X was 3 to 4. During the year, 10 boys and twice as many girls transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of boys to girls was 4 to 5, how many boys were there in high school X at the beginning of the year?  Choose the correct choice from the following options:  A) 70  B) 120  C) 100  D) 90  E) 110
let the total number of boys and girls at the beginning of the year be 3x and 4x respectively.   now 10 boys and 20 girls are transferred to another school. thus no. of boys and girls students left in the school X are 3x-10 and 4x-20 respectively. the ratio of these boys and girls students = 4/5   thus we have (3x-10)/(4x-20) = 4/5   15x-50= 16x-80   x=30   thus total no. of boys at the beginning of the year =4(30)= 120   Answer is option 120
<result>B</result>
At the beginning of the year, the ratio of boys to girls in high school X was 3 to 4. During the year, 10 boys and twice as many girls transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of boys to girls was 4 to 5, how many boys were there in high school X at the beginning of the year?