The average weight of a group of boys is 30 kg. After a boy weighing 35 kg joins the group, the average weight of the group increases by 1 kg. How many boys were there in the group originally?

Introduction / Context:
This problem shows how adding one new value above the existing average increases the group average. You are asked to infer the original group size based on the change in average caused by the new member.

Given Data / Assumptions:
- The original average weight of the boys is 30 kg.
- A new boy with weight 35 kg joins the group.
- After he joins, the average weight increases by 1 kg to 31 kg.
- We must find the original number of boys in the group.

Concept / Approach:
Let the original number of boys be n. The original total weight is 30n. After adding a boy of 35 kg, the new total weight is 30n + 35 and the number of boys becomes n + 1. The new average is 31, so (30n + 35) / (n + 1) = 31. Solving this equation gives n.

Step-by-Step Solution:
Step 1: Let the original number of boys be n. Step 2: Original total weight = 30n kg. Step 3: After adding the new boy, total weight = 30n + 35 kg and number of boys = n + 1. Step 4: New average is 31, so (30n + 35) / (n + 1) = 31. Step 5: Multiply both sides by n + 1: 30n + 35 = 31(n + 1). Step 6: Expand the right side: 30n + 35 = 31n + 31. Step 7: Rearrange: 35 - 31 = 31n - 30n, so 4 = n. Step 8: Therefore, there were originally 4 boys in the group.

Verification / Alternative check:
If there were 4 boys with average weight 30 kg, total weight is 120 kg. Adding a boy of 35 kg gives 155 kg over 5 boys. The new average is 155 / 5 = 31 kg, which matches the condition. So n = 4 is correct.

Why Other Options Are Wrong:
- Option 6: If n = 6, original total is 180, new total 215, and new average 215 / 7, which is not 31.

- Option 8: If n = 8, original total is 240, new total 275, and new average 275 / 9, again not equal to 31.

- Option 5: If n = 5, original total is 150, new total 185, and new average 185 / 6, which is not 31.

Common Pitfalls:
Some students incorrectly assume that the change in average compares directly with the difference between 30 and 35 and try proportional reasoning instead of setting up an equation. Others forget to change both the numerator and the denominator when the new boy is added. Always reflect both the change in total weight and the change in group size.

Final Answer:
Originally there were 4 boys in the group.