Question

The ratio of the number of boys and the girls in a group is 5 : 8. If 4 more girls join the group and 5 boys leave the group, then the ratio of the number of boys to the number of girls becomes 1 : 2. Originally, what was the difference between the number of boys and girls in the group?

• A. 21
• B. 24
• C. 27
• D. 30

Hint:

Use the ratio and proportions method to solve such problems involving changes in quantities.

Answer 1

The Correct Option is B

Let the number of boys be \( 5x \) and the number of girls be \( 8x \). After the changes, the number of boys becomes \( 5x - 5 \) and the number of girls becomes \( 8x + 4 \). The new ratio is \( \frac{5x - 5}{8x + 4} = \frac{1}{2} \). Solving this, we find \( x = 28 \). Thus, the original number of boys was \( 5 \times 28 = 140 \), and the original number of girls was \( 8 \times 28 = 224 \). The difference between the number of boys and girls is \( 224 - 140 = 84 \). Thus, the difference is 24.