In a school, the ratio of boys to girls is $5 : 2$ . After the school added 6 more girls, the ratio becomes $5 : 3$ . What is the initial number of boys in the school?

hard MCQ 4 marks Class 6 · Mathematics · Ratio and Proportion

Answer

The correct answer is 30 — Initial number of boys = $5 k = 5 \times 6 = 30$ .

Step-by-step solution

Let the initial number of boys be $5 k$ and girls be $2 k$ .
After adding 6 girls, girls become $2 k + 6$ .
The new ratio is $5 k : (2 k + 6) = 5 : 3$ . Set up the proportion $\frac{5 k}{2 k + 6} = \frac{5}{3}$ .
Cross multiply: $5 k \times 3 = 5 \times (2 k + 6)$ .
Simplify: $15 k = 10 k + 30$ .
Subtract $10 k$ from both sides: $5 k = 30$ .
Solve for $k$ : $k = 6$ .
Initial number of boys = $5 k = 5 \times 6 = 30$ .

Common mistake: Adding 6 to the boys instead of the girls.

Concept tested: Changing a ratio after adding members