The average weight of 50 boys in a class is 45 kg. When one boy leaves the class, the average weight reduces by 0.1 kg. What is the weight of the boy who left the class, in kilograms?

Introduction / Context:
This aptitude problem explores how removing one member from a group affects the average. You are given the average weight of 50 boys and told that when one boy leaves, the average decreases by 0.1 kg. Using this information you must determine the weight of the boy who left. This type of question checks understanding of how totals and averages interact when elements are added or removed.

Given Data / Assumptions:
- There are initially 50 boys in the class.
- Average weight of these 50 boys is 45 kg.
- After one boy leaves, the class has 49 boys.
- The new average weight is 0.1 kg lower, that is 44.9 kg.
- We must find the weight of the boy who left the class.

Concept / Approach:
The total weight of the group is always equal to average multiplied by the number of boys. We first calculate the total weight of all 50 boys. Then we compute the total weight after one boy leaves using the new average and 49 boys. The difference between the original total and the new total gives the weight of the boy who left. This approach is straightforward and widely used in average problems involving entry or exit of members.

Step-by-Step Solution:
Step 1: Initial average weight of 50 boys = 45 kg.Step 2: Initial total weight of all 50 boys = 50 * 45 = 2250 kg.Step 3: After one boy leaves, the new average is 45 - 0.1 = 44.9 kg.Step 4: Number of boys left in the class = 49.Step 5: New total weight after the boy leaves = 49 * 44.9 kg.Step 6: Compute the new total: 49 * 44.9 = 2200.1 kg.Step 7: Weight of the boy who left = initial total weight - new total weight.Step 8: Weight of the boy who left = 2250 - 2200.1 = 49.9 kg.

Verification / Alternative check:
We can verify by reasoning about the changed average. Removing a boy slightly lighter than the original average would increase the average, while removing a boy heavier than the original average would decrease it. The average dropped from 45 to 44.9, so the removed boy must be slightly heavier than the new average but slightly lighter than some of the others. Computing the exact difference between totals gives 49.9 kg, and recomputing the new average 2200.1 / 49 confirms the value of 44.9 kg exactly.

Why Other Options Are Wrong:
Weights like 50 kg or 49 kg would produce different new totals and would not reduce the average by exactly 0.1 kg. For example, if the boy weighed 50 kg, the new total would be 2250 - 50 = 2200 kg and the new average would be 2200 / 49 which is slightly less than 44.9, not exactly equal. Similar inconsistencies arise with the other options. Only 49.9 kg produces the correct new average of 44.9 kg.

Common Pitfalls:
Students sometimes subtract 0.1 kg directly from 45 and assume that this is the boy weight, which is incorrect because that value is an average, not an individual weight. Others mistakenly treat 49 as the divisor instead of 50 when computing the original total. Always compute the original and new totals, then use their difference to find the individual weight that left the group.

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