In a class of 39 students, the ratio of boys to girls is 2 : 1. Radhika is one of the girls. She ranks 15th from the top among all students and 8th from the bottom among the girls. How many boys are there below Radhika in the overall class ranking?

Introduction / Context:
This question blends ratio concepts with positional ranking and counting. It is common in aptitude tests where you must interpret ranks from both the top and bottom, and combine this with the total number of students and the ratio of boys to girls to determine how many of a particular group lie above or below a given person.

Given Data / Assumptions:
• Total students in the class = 39.
• Ratio of boys : girls = 2 : 1.
• Radhika is a girl.
• Radhika is 15th from the top among all students.
• Radhika is 8th from the bottom among the girls.

Concept / Approach:
First, convert the ratio of boys to girls into exact numbers. Then, use Radhika’s rank among girls from the bottom to find her rank among girls from the top. Once we know how many girls are above her, we subtract that from her overall rank to find how many boys are above her. Finally, subtract boys above from total boys to get the number of boys below her.

Step-by-Step Solution:
Step 1: Let boys : girls = 2 : 1. Total parts = 3. Since total students are 39, boys = 2/3 * 39 = 26 and girls = 1/3 * 39 = 13.Step 2: Radhika is a girl and is 8th from the bottom among 13 girls.Step 3: Her rank among girls from the top is 13 − 8 + 1 = 6. So there are 5 girls above her.Step 4: Radhika is 15th from the top in the entire class, so among the first 15 students: 5 are girls above her and the 6th is Radhika herself.Step 5: Therefore, number of boys above Radhika = 15 − 6 = 9.Step 6: Total boys = 26, so boys below Radhika = 26 − 9 = 17.

Verification / Alternative check:
We can check consistency: there are 13 girls; 5 above Radhika, 1 is Radhika, and 7 below her among girls, which matches the 8th-from-bottom statement. In the entire class, students below Radhika are 39 − 15 = 24; among these, 7 are girls and 17 are boys, which exactly matches the boys-below result we computed. All counts are consistent.

Why Other Options Are Wrong:
Option 9 is the number of boys above her, not below her.
Options 11 and 15 do not satisfy the total count of boys and the distribution above and below Radhika when you work through the details. They contradict either the total number of boys or the given ranking information.

Common Pitfalls:
Students often confuse ranks from the top and bottom, forgetting to add 1 when converting between them. Another typical mistake is to ignore that the ratio of boys to girls must first be converted into actual numbers before counting people above and below a specific student. Careful step-by-step reasoning avoids these errors.

Final Answer:
The number of boys below Radhika in the overall ranking is 17.