Percentages and ratios — festival participation: Find the fraction of all students who took part. In an institute fete, 1/5 of the girls and 1/8 of the boys participated. Determine the overall fraction of the total student body that participated. Choose the correct fraction/value.

Given data

• Fraction of girls who participated = 1/5 of all girls.
• Fraction of boys who participated = 1/8 of all boys.

Concept/Approach
Let the numbers of girls and boys be G and B. Then participants are G/5 + B/8 and the total students are G + B. The overall fraction is (G/5 + B/8) / (G + B), which depends on the (unknown) ratio G:B.

Step-by-step reasoning
Overall fraction = (G/5 + B/8) ÷ (G + B) = (8G + 5B) / (40(G + B)).This varies with G and B (e.g., if G = B, fraction = 13/80; if G = 2B, it becomes 21/120 = 7/40).

Conclusion
The exact fraction cannot be uniquely determined without the girl-to-boy ratio.

Final Answer
Data inadequate