Understanding the Average Weight Problem

This problem asks us to find Rohan's specific weight given the average weight of a group (Rohan plus three friends) and a relationship between Rohan's weight and the average weight of his friends.

Step-by-Step Solution

1. Calculate the Total Weight of the Group:

   We know the average weight of Rohan and his three friends (4 people in total) is 62 kg. The total weight is calculated by multiplying the average weight by the number of people.

   $$ \text{Total Weight} = \text{Average Weight} \times \text{Number of People} $$

   $$ \text{Total Weight} = 62 \, \text{kg} \times 4 = 248 \, \text{kg} $$

   So, the combined weight of Rohan and his three friends is 248 kg.

2. Set Up Algebraic Equations:

   Let $R$ represent Rohan's weight in kg.

   Let $AvgF$ represent the average weight of Rohan's three friends in kg.

   The problem states that Rohan's weight is 8 kg more than the average weight of his three friends. This can be written as:

   $$ R = AvgF + 8 \, \text{kg} $$

   We can rearrange this to express the average weight of the friends in terms of Rohan's weight:

   $$ AvgF = R - 8 \, \text{kg} $$

   We also know the total weight of the group is 248 kg. The total weight is the sum of Rohan's weight and the combined weight of his three friends. The combined weight of the three friends is $3 \times AvgF$. So, the equation for the total weight is:

   $$ R + (3 \times AvgF) = 248 \, \text{kg} $$

3. Solve for Rohan's Weight:

   Now we substitute the expression for $AvgF$ (from step 2) into the total weight equation:

   $$ R + 3 \times (R - 8) = 248 $$

   Distribute the 3:

   $$ R + 3R - 24 = 248 $$

   Combine the terms with $R$:

   $$ 4R - 24 = 248 $$

   Add 24 to both sides of the equation to isolate the term with $R$:

   $$ 4R = 248 + 24 $$

   $$ 4R = 272 $$

   Finally, divide by 4 to find Rohan's weight ($R$):

   $$ R = \frac{272}{4} $$

   $$ R = 68 $$

4. Final Answer:

   Rohan's weight is 68 kg.