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]

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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. Total Group = Specific Part × \frac{Denominator}{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 (4/7) of the total boys participated. - Let total boys be B. So, (4/7) × B = 124. - B = (124 × 7/4) = 31 × 7 = 217. 4. Calculate the total number of girls in the school: - We are given that (6/11) of the total girls participated. - Let total girls be G. So, (6/11) × G = 84. - G = (84 × 11/6) = 14 × 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 × ((7/4)) = 217. The remaining participants are girls: 208 - 124 = 84. For girls: 84 × ((11/6)) = 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.

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