Question

In a class of 58 students, the rank of Miss X is 14 from the top. Miss Y has better rank than Miss X and there are 5 students ranks between them. Then the rank of Miss Y from the bottom is

• A. 39
• B. 38
• C. 51
• D. 49

Hint:

Whenever rank from the top and rank from the bottom are involved, remember: \[ \text{Top Rank}+\text{Bottom Rank}=N+1 \] where \(N\) is the total number of students.

Answer 1

The Correct Option is C

Concept: If the rank from the top is known, then \[ \text{Rank from Bottom} = \text{Total Students} - \text{Rank from Top} + 1 \]

Step 1: Find Miss Y's rank from the top.
Miss X is \(14^{th}\) from the top. Miss Y has a better rank than Miss X and there are 5 students between them. Therefore, \[ \text{Rank of Y from top} = 14-(5+1) = 8 \] Thus Miss Y is \(8^{th}\) from the top.

Step 2: Convert top rank into bottom rank.
Total students \(=58\). Hence, \[ \text{Rank from bottom} = 58-8+1 = 51 \] Therefore, \[ \boxed{51} \]