In a school, 1/4 of the boys and 3/8 of the girls participated in the annual sports day. What fractional part of the total student strength participated?

Introduction / Context:
This question examines whether a unique fraction of total participants can be determined without knowing the ratio of boys to girls. It highlights dependence on missing composition data when combining parts of different groups.

Given Data / Assumptions:

• Boys = B, Girls = G, Total = B + G.
• Participants = (1/4)B + (3/8)G.
• No information is given about the ratio B:G.

Concept / Approach:
To get a fraction of total, compute [(1/4)B + (3/8)G] / (B + G). Without a relation between B and G, this expression is not uniquely determined, because it changes with the composition of the student body.

Step-by-Step Solution:

Verification / Alternative check:
Try examples: If B = G, then F = ((1/4) + (3/8)) / 2 in normalized terms, different from when B ≠ G. Changing B:G alters F, proving non-uniqueness.

Why Other Options Are Wrong:

• 32%, 20%, 36%, 28%: Each is a fixed number, which cannot be guaranteed without knowing B:G.

Common Pitfalls:

• Assuming equal numbers of boys and girls when not stated.
• Adding fractions as if they referred to the same base group.

Final Answer:
Data inadequate