In a class, the number of boys exceeds the number of girls by 12% of the total class strength. What is the ratio of boys to girls?

Introduction / Context:
This problem assesses understanding of how to convert a verbal comparison involving a percentage of the total into a concrete ratio between two parts (boys and girls). Many learners mix up “percent of total” with “percent of one part,” so translating the statement into algebra relative to total strength is the key.

Given Data / Assumptions:

• Boys are more than girls by 12% of the total class strength.
• Total strength is the sum of boys and girls only.
• We must express boys : girls in simplest whole-number form.

Concept / Approach:
Let total = T, boys = B, girls = G. We are told B − G = 0.12*T and B + G = T. Solving these two linear relations gives B and G in terms of T. Finally, convert B:G to a whole-number ratio.

Step-by-Step Solution:
B − G = 0.12TB + G = TAdd both: 2B = 1.12T ⇒ B = 0.56TThen G = T − B = T − 0.56T = 0.44TRatio B : G = 0.56T : 0.44T = 56 : 44 = 14 : 11

Verification / Alternative check:
Check the difference if B:G = 14:11 out of total 25 parts. Difference = 3 parts; 3/25 of total = 12%, which matches the given condition.

Why Other Options Are Wrong:
11 : 14 and 25 : 28 imply boys fewer or the same proportion as girls; 28 : 25 and 7 : 6 give a difference larger than 12% of total.

Common Pitfalls:
Taking 12% of girls (or boys) instead of 12% of total; skipping the system B − G and B + G and thereby miscomputing the ratio.

Final Answer:
14 : 11