In a class the number of girls is 20% more than that of the boys. The strength of the class is 66. If 4 more girls are admitted to the class, the ratio of the number of boys to that of the girls is

### Concept & Percentage Proportions To solve problems relating totals and relative percentages, express both quantities in terms of a single variable. The total sum of these expressions equals the overall strength. $$ \text{Total} = \text{Boys} + \text{Girls} $$ ### Step-by-Step Solution 1. Let the number of boys in the class be $x$. 2. The number of girls is $20\%$ more than the boys, which can be written as $x + 0.20x = 1.2x$. 3. The total strength of the class is $66$. Set up the equation: $$ x + 1.2x = 66 $$ 4. Solve for $x$: $$ 2.2x = 66 $$ $$ x = \frac{66}{2.2} = 30 $$ 5. So, there are $30$ boys. The number of girls is $1.2 \times 30 = 36$. 6. If $4$ more girls are admitted, the new number of girls becomes $36 + 4 = 40$. 7. The new ratio of boys to girls is: $$ \frac{\text{Boys}}{\text{Girls}} = \frac{30}{40} = \frac{3}{4} $$ 8. This corresponds to the ratio $3 : 4$. ### Exam Strategy & Shortcut Instead of decimals, use proportional parts. Let boys be $100$ units. Girls are $120$ units. The ratio of Boys:Girls is $100:120 = 5:6$. Total parts = $5 + 6 = 11$ parts. Since $11$ parts = $66$ students, $1$ part = $6$ students. Boys = $5 \times 6 = 30$. Girls = $6 \times 6 = 36$. New girls = $36 + 4 = 40$. New ratio = $30 : 40 = 3 : 4$. ### Common Pitfall A common error is adding the $4$ new students to the boys' count instead of the girls, or calculating the final ratio backwards as girls to boys ($4 : 3$). Always pay close attention to the final order requested in the prompt. ### Final Answer Therefore, the correct answer is **3 : 4**.