Question

At a school event, there were 96 girls. The ratio of the number of girls to the number of boys was 4 : 5. After some time, some boys arrived and th ratio became 2 : 3. How many boys arrived?

Answer 1

The girls are 4/9 of the total number of boys and girls, so the total number is 9×96/4=216 and there are 5/9×216=120 boys.
Let the extra number of boys be b, then the total becomes 216+b. We have 96 girls and 120+b boys.
The ratio 2/3=96/(120+b).
Cross multiplying: 2(120+b)=3×96=288.
240+2b=288, 2b=288-240=48, b=24.
So 24 boys arrived.