The average weight of 8 persons increases by 2.5 kg when a new person replaces one of the original 8, whose weight was 65 kg. What is the weight (in kilograms) of the new person who joined the group?

Introduction / Context:
This question examines how the average of a group changes when one member is replaced by another person of a different weight. It combines average concepts with change in total value when one observation is removed and another is added. Understanding the relationship between total weight and average weight is key to solving such problems quickly in aptitude exams.

Given Data / Assumptions:

• Number of persons initially = 8.
• Weight of the person who leaves = 65 kg.
• After replacement, the average weight of the 8 persons increases by 2.5 kg.
• Let the original average weight be A kg.
• Let the weight of the new person be W kg.

Concept / Approach:
If the average increases by 2.5 kg for 8 persons, the total weight of the group must increase by: increase in total = number of persons * increase in average. We compute this increase and relate it to the difference between the new person's weight and the old person's weight. This directly gives us the new weight without needing the original average explicitly.

Step-by-Step Solution:
Step 1: Original total weight = 8 * A. Step 2: New average = A + 2.5 kg. Step 3: New total weight = 8 * (A + 2.5) = 8A + 20. Step 4: When we replace the 65 kg person with the new person of weight W, new total weight = (original total) - 65 + W. So, 8A + 20 = 8A - 65 + W. Step 5: Cancel 8A on both sides: 20 = -65 + W. Step 6: Therefore, W = 20 + 65 = 85 kg.
Verification / Alternative check:
Increase in average = 2.5 kg for 8 persons, so total increase = 8 * 2.5 = 20 kg. This increase in total weight comes entirely from replacing 65 kg with W kg, so W - 65 = 20. Thus W = 85 kg, which confirms our earlier result.
Why Other Options Are Wrong:
Option A (70 kg), B (75 kg), C (80 kg) and E (90 kg) do not yield a net increase of exactly 20 kg when compared to 65 kg, so they would not produce a 2.5 kg increase in average for 8 persons. For example, if W = 80 kg, increase = 15 kg, total increase per person = 15 / 8 ≈ 1.875 kg, not 2.5 kg.
Common Pitfalls:
A common mistake is to try to compute the original average explicitly, which is unnecessary and may introduce errors. Another error is forgetting that the average change for the whole group scales the total change by the number of people.
Final Answer:
The weight of the new person who joins the group is 85 kg.