Question

The ratio of boys to girls in a school is 7:5. If 20 more girls join the school, the new ratio of boys to girls becomes 7:6. What is the total number of students in the school initially?

• A. 200
• B. 240
• C. 300
• D. 360

Answer 1

Answer:

B. 240

Let the initial numbers of boys and girls be:

$7x \text{ and } 5x$

After 20 girls join:

$\frac{7x}{5x+20}=\frac{7}{6}$

$\frac{7x}{5x+20}=\frac{7}{6}$

Cross multiply:

42x = 35x + 140
7x = 140
x = 20

Initial total students:

$7x + 5x = 12x = 12 \times 20 = 240$

Therefore, the initial number of students was 240.