The average weight of 50 boys in a class is 45 kg. When one boy leaves the class, the average weight decreases by 100 g. What is the weight (in kg) of the boy who left the class?

Introduction / Context:
This question is another average and total weight problem. It involves a group whose average weight is known, and when one member leaves, the average changes slightly. The task is to deduce the weight of the person who left using the change in total weight implied by the change in the average.

Given Data / Assumptions:
- Original number of boys in the class = 50. - Original average weight = 45 kg. - After one boy leaves, number of boys = 49. - New average weight = 45 kg - 0.1 kg = 44.9 kg (since 100 g = 0.1 kg). - We need to find the weight of the boy who left.

Concept / Approach:
Average weight equals total weight divided by number of boys. Using the initial average and count, we compute the initial total weight. Using the new average and count, we compute the new total weight. The difference between these two totals equals the weight of the boy who left. This is a direct application of the average formula and simple subtraction.

Step-by-Step Solution:
Step 1: Original average weight = 45 kg, number of boys = 50. Step 2: Original total weight = 45 * 50 = 2250 kg. Step 3: After one boy leaves, number of boys = 49. Step 4: New average weight = 44.9 kg. Step 5: New total weight = 44.9 * 49. Step 6: Compute new total weight: 44.9 * 49 = 44.9 * (50 - 1) = 44.9 * 50 - 44.9 = 2245 - 44.9 = 2200.1 kg. Step 7: Weight of the boy who left = original total weight - new total weight. Step 8: Weight of boy = 2250 - 2200.1 = 49.9 kg.

Verification / Alternative check:
We can reconstruct the situation. Suppose the boy who left weighed 49.9 kg. Then total initial weight is 2200.1 + 49.9 = 2250 kg, and average for 50 boys is 2250 / 50 = 45 kg as given. After he leaves, 49 boys remain with total weight 2200.1 kg, giving an average of 2200.1 / 49 = 44.9 kg, which is 0.1 kg less than the original average. This matches the entire story perfectly and confirms the answer.

Why Other Options Are Wrong:
Option A (50 kg): Would result in a new total of 2250 - 50 = 2200 and a new average of 2200 / 49, not 44.9 kg. Option B (50.8 kg): Gives a larger reduction than required. Option C (49 kg): Leads to a different new average than the one given. Option E (52 kg): Too heavy and would change the average more than 0.1 kg.

Common Pitfalls:
Some students incorrectly subtract 0.1 kg from a randomly chosen boy's weight or from the total instead of computing the new total carefully. Others mistakenly assume that the difference in average directly equals the weight of the boy who left, which is not correct because the group size changes as well. The correct approach is always to compute the total weights before and after, then subtract to find the missing individual weight.

Final Answer:
The weight of the boy who left the class is 49.9 kg.