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 (before he joined)?

Introduction / Context:
This problem combines average calculations with reasoning about how a new member affects the average. The original group of boys has an average weight of 30 kg. After a boy weighing 35 kg joins, the average increases by 1 kg to 31 kg. We are asked to determine how many boys were in the group before the new boy joined.

Given Data / Assumptions:

• Original average weight = 30 kg.
• A new boy with weight = 35 kg joins the group.
• New average weight becomes 31 kg.
• Let the number of boys originally be n.
• After joining, the number of boys becomes n + 1.

Concept / Approach:
We use the average formula: average = total weight / number of persons. We express the original total weight as 30n. When the new boy joins, the total becomes 30n + 35, and the new average is 31 over n + 1 boys. Setting up and solving the equation derived from this situation will give us n, the original count of boys.

Step-by-Step Solution:
Step 1: Let the original number of boys be n. Original total weight = 30n. Step 2: After the boy of 35 kg joins, total weight = 30n + 35. Number of boys now = n + 1. Step 3: New average = 31 kg. So (30n + 35) / (n + 1) = 31. Step 4: Multiply both sides by (n + 1) to clear the denominator. 30n + 35 = 31(n + 1). Step 5: Expand the right-hand side. 30n + 35 = 31n + 31. Step 6: Rearrange to solve for n. 31n − 30n = 35 − 31 → n = 4.
Verification / Alternative check:
Original group: n = 4 boys, average = 30 kg, total weight = 4 * 30 = 120 kg. Add the new boy: total weight = 120 + 35 = 155 kg, number of boys = 5. New average = 155 / 5 = 31 kg, which is exactly 1 kg more than 30, matching the condition.
Why Other Options Are Wrong:
If n = 5 originally, original total weight = 150 kg, new total = 185 kg, new average = 185 / 6 ≈ 30.83, not 31. Similar contradictions arise for n = 6, 7 or 8, none giving precisely 31 as the new average.
Common Pitfalls:
Some students incorrectly assume that the difference between 35 and the new average (31) directly gives the number of boys, which is not correct without setting up the equation. Others may mistakenly use 30 instead of 31 when multiplying by the new number of boys.
Final Answer:
The number of boys in the original group was 4.