In a class of 180 students, the number of girls is twice the number of boys. Rupesh, who is a boy, ranks 34th from the top. If there are 18 girls ahead of Rupesh in the ranking, how many boys are there after him in rank?

Introduction / Context:
This is a combined arithmetic and ranking question involving two groups, boys and girls, within a class. You are given the ratio of girls to boys, the total strength, the rank of one boy and the number of girls ahead of him. The task is to determine how many boys are ranked after him. Such questions test your ability to translate word statements into equations and then analyse the composition of the group above and below a particular rank.

Given Data / Assumptions:

- Total number of students in the class is 180.- Girls are twice the number of boys.- Rupesh is a boy and ranks 34th from the top.- There are 18 girls ahead of Rupesh.

Concept / Approach:
First, use the ratio of girls to boys to determine the exact number of boys and girls. Next, use the information about Rupesh's position and the number of girls ahead of him to deduce how many boys are ahead of him. Since he himself is a boy, the remaining boys must lie after him in rank. Subtracting the number of boys ahead plus Rupesh from the total number of boys gives the required answer.

Step-by-Step Solution:
Step 1: Let the number of boys be B and the number of girls be G.Step 2: Given that girls are twice the boys, so G = 2B.Step 3: Total students are 180, so B + G = 180.Step 4: Substitute G = 2B into B + G = 180 to get B + 2B = 180.Step 5: Simplify to 3B = 180, so B = 180 / 3 = 60.Step 6: Then G = 2B = 2 * 60 = 120.Step 7: Rupesh ranks 34th from the top and there are 18 girls ahead of him. So the number of students ahead of him is 33, and among these 33, 18 are girls.Step 8: Therefore, the number of boys ahead of Rupesh is 33 - 18 = 15.Step 9: Since Rupesh himself is a boy, the total number of boys who are not ahead of him is 60 - 15 = 45.Step 10: This group of 45 boys includes Rupesh. So the number of boys after him in rank is 45 - 1 = 44.

Verification / Alternative check:
We can cross-check by counting boys in all three segments: boys ahead of Rupesh (15), Rupesh himself (1) and boys after him (44). The total is 15 + 1 + 44 = 60, which matches the calculated number of boys. This consistency confirms that the reasoning is correct.

Why Other Options Are Wrong:
Option 45 would incorrectly count Rupesh as being after himself. Option 60 is the total number of boys in the class and not the number after him. Option cannot be determined is incorrect because the information given is sufficient to compute the exact figure. Only 44 matches both the ratio and the ranking constraints.

Common Pitfalls:
Students sometimes forget to subtract Rupesh when counting boys after him, or they miscount the number of boys ahead by not excluding Rupesh from the first 34 ranks. Another source of error is incorrectly solving the ratio equation for boys and girls. Keeping track of each segment clearly prevents these mistakes.

Final Answer:
The number of boys who are ranked after Rupesh is 44.