4/7th of the boys and 6/11th of girls of a school participated in marathon. If the number of participating students is 208 out of which 124 are boys, what is the total, number of students in the school? [NICL—AAO Exam, 2015]

### Concept & Algebraic Manipulation We can find the total number of individuals in a specific group if we know the fractional amount that represents a participating subset of that group. $$ \text{Total Group} = \text{Specific Part} \times \frac{\text{Denominator}}{\text{Numerator}} $$ ### Step-by-Step Solution 1. Identify the given values for participants: - Total participating students = 208 - Participating boys = 124 2. Calculate the number of participating girls: - Participating girls = Total participants - Participating boys - Participating girls = $208 - 124 = 84$ 3. Calculate the total number of boys in the school: - We are given that $\frac{4}{7}$ of the total boys participated. - Let total boys be $B$. So, $\frac{4}{7} \times B = 124$. - $B = \frac{124 \times 7}{4} = 31 \times 7 = 217$. 4. Calculate the total number of girls in the school: - We are given that $\frac{6}{11}$ of the total girls participated. - Let total girls be $G$. So, $\frac{6}{11} \times G = 84$. - $G = \frac{84 \times 11}{6} = 14 \times 11 = 154$. 5. Determine the total number of students in the school: - Total students = Total boys + Total girls - Total students = $217 + 154 = 371$. ### Exam Strategy & Shortcut Solve for the subgroups independently using reciprocal fractions. For boys: $124 \times \left(\frac{7}{4}\right) = 217$. The remaining participants are girls: $208 - 124 = 84$. For girls: $84 \times \left(\frac{11}{6}\right) = 154$. Add them together: $217 + 154 = 371$. ### Common Pitfall A typical error is applying the total participant number (208) to the fractions directly or cross-mixing the fractions, ignoring the explicit breakdown of boys and girls which have completely different fractional participation rates. ### Final Answer Therefore, the correct answer is **371**.