Ranking and counts – In a class of 180 where girls are twice the number of boys, Rupesh (a boy) is 34th from the top. If 18 girls are ahead of him, how many boys are ranked below him?

Introduction / Context:This is a classic ranking and composition problem combining total counts, ratios, and position-based reasoning.

Given Data / Assumptions:

• Total students = 180.
• Girls = 2 × boys ⇒ B + 2B = 180 ⇒ B = 60, G = 120.
• Rupesh is a boy, ranked 34th from top.
• Girls ahead of him = 18.

Concept / Approach:Use rank to get counts above: 33 students are ahead of him. Subtract girls-ahead to get boys-ahead. Then subtract (boys-ahead + Rupesh himself) from total boys to get boys-below.

Step-by-Step Solution:Ahead of Rupesh (total) = 34 - 1 = 33.Boys ahead = 33 - 18 = 15.Total boys = 60.Boys below = 60 - (boys ahead + 1) = 60 - (15 + 1) = 44.

Verification / Alternative check:Boys at or above Rupesh = 16; remaining boys must be below = 44. Totals reconcile: 16 + 44 = 60.

Why Other Options Are Wrong:45/60 miscount either the boys ahead or forget to include Rupesh himself. “Cannot be determined” is incorrect given complete information.

Common Pitfalls:Forgetting to include the candidate when subtracting from total boys, or mixing the girls-ahead with total-ahead wrongly.

Final Answer:44