Pass–fail ratio with partial ranks – Among passed students: Neeta is 22nd from top; Kalyan is 5 ranks below Neeta and 34th from the bottom. The class pass:fail ratio is 4:1. How many students are in the class?

Introduction / Context:
This combines two-sided rank within the passed subgroup with an overall pass:fail ratio to determine total class size.

Given Data / Assumptions:

• Neeta (passed) = 22nd from top.
• Kalyan is 5 ranks below Neeta → 27th from top among passed.
• Kalyan is 34th from bottom among passed.
• Pass : Fail = 4 : 1.

Concept / Approach:
First, compute the number of passed students (P) using Kalyan’s two-sided rank: P = 27 + 34 − 1. Then use the given ratio to get total N.

Step-by-Step Solution:
P = 27 + 34 − 1 = 60.Pass:Fail = 4:1 → P = 4k ⇒ 60 = 4k ⇒ k = 15.Total N = 5k = 75.

Verification / Alternative check:
Failed students = N − P = 75 − 60 = 15, matching the 4:1 ratio.

Why Other Options Are Wrong:
60 is the passed count, not total; 90 contradicts the computed ratio; “Data inadequate” is incorrect because the subgroup data suffices.

Common Pitfalls:
Using Neeta’s rank to compute P; forgetting to subtract one in two-sided ranks.

Final Answer:
75