Calculating Rank from the Bottom

This problem asks us to find Ayush's position from the bottom of the class, given his total number of classmates and his rank from the top.

Understanding the Concept

When we talk about ranks in a group (like a class), the total number of people is related to the rank from the top and the rank from the bottom. If someone is rank '$R_{top}$' from the top and rank '$R_{bottom}$' from the bottom, the total number of people '$N$' in the group can be calculated using the formula:

$N = R_{top} + R_{bottom} - 1$

The '$-1$' is included because the person themselves is counted in both the top rank and the bottom rank.

Given Information

• Total number of students in the class ($N$): $45$
• Ayush's rank from the top ($R_{top}$): $15$

Applying the Formula

We need to find Ayush's rank from the bottom ($R_{bottom}$). We can rearrange the formula above:

$R_{bottom} = N - R_{top} + 1$

Step-by-Step Calculation

1. Substitute the given values into the rearranged formula:

   $R_{bottom} = 45 - 15 + 1$

2. First, subtract the rank from the top from the total number of students:

   $45 - 15 = 30$

3. Then, add $1$ to include Ayush's own position:

   $30 + 1 = 31$

Result

Therefore, Ayush's rank from the bottom is $31$.