In a class of 60 students, the ratio of boys to girls participating in the annual sports is 3 : 2. The number of girls not participating is 5 more than the number of boys not participating. If the number of boys participating is 15, how many girls are there in the class?

Introduction / Context:
This question combines ratios, total counts, and participation information to test logical reasoning about a class of students. We know the total number of students, the ratio of participating boys to participating girls, and how many more girls than boys are not participating. We are also told the number of boys who do participate. The goal is to determine the total number of girls in the class. Such questions are standard in bank and SSC aptitude exams.

Given Data / Assumptions:

• Total students in the class = 60.
• Ratio of participating boys to participating girls is 3 : 2.
• Number of boys participating = 15.
• Number of girls not participating is 5 more than number of boys not participating.
• We assume every student is either a boy or a girl and either participates or does not participate.

Concept / Approach:
We first use the participation ratio to determine how many girls participate. Then we set up variables for total boys and girls and express non-participating counts in terms of these. The relationship between non-participating girls and boys helps us form an equation, which we solve together with the total students equation to find the total number of girls in the class.

Step-by-Step Solution:
Step 1: Let total boys be B and total girls be G. So B + G = 60.Step 2: Participating boys to participating girls is 3 : 2, and participating boys are 15.Step 3: If 3 parts correspond to 15 boys, then 1 part = 5 and 2 parts = 10 girls participating.Step 4: Boys not participating = B - 15. Girls not participating = G - 10.Step 5: The number of girls not participating is 5 more than the number of boys not participating, so G - 10 = (B - 15) + 5.Step 6: Simplify the relation: G - 10 = B - 10, which gives G = B.Step 7: Substitute G = B into B + G = 60 to obtain 2B = 60, so B = 30 and G = 30.Step 8: Therefore, there are 30 girls in the class.

Verification / Alternative check:
With B = 30 and G = 30, check participation: boys participating = 15 (given), so boys not participating = 30 - 15 = 15. Girls participating = 10, so girls not participating = 30 - 10 = 20. The condition “girls not participating are 5 more than boys not participating” becomes 20 = 15 + 5, which is correct. The ratio of participating boys to participating girls is 15 : 10 = 3 : 2, matching the problem statement. All conditions are satisfied.

Why Other Options Are Wrong:
Option A (20) and Option B (25): These values for G, combined with B = 60 - G, fail to satisfy both the ratio and the non-participation difference simultaneously.
Option D (Data inadequate): This is incorrect because the given data are sufficient to uniquely determine B and G through the equations.

Common Pitfalls:
Some students mistakenly apply the ratio 3 : 2 to total boys and girls instead of applying it only to participants. Others forget to link the non-participation counts correctly, or they mis-handle the equation G - 10 = B - 10. Writing clear expressions for participants and non-participants separately for boys and girls helps avoid such mistakes.

Final Answer:
There are 30 girls in the class.