The average weight of 8 persons increases by 2.5 kg when a new person replaces one of them who weighs 65 kg. What is the weight of the new person?

Introduction / Context:
This question tests the concept of average and how it changes when one value in a group is replaced by another. It appears frequently in aptitude tests for bank PO, SSC, and campus placements. Understanding how the average shifts allows us to find the weight of the new person who joins the group of eight and causes a known increase in the average weight.

Given Data / Assumptions:
- Number of persons in the group = 8.
- Weight of the person who leaves the group = 65 kg.
- The new person joins in place of this person.
- The average weight of the 8 persons increases by 2.5 kg after the replacement.
- We need to find the weight of the new person in kilograms.

Concept / Approach:
When the average of a group changes due to replacing one member, the net change in total weight can be computed by multiplying the change in average by the number of members. That net change must be equal to the difference between the weight of the new person and the weight of the person who left. Using this relation, we can find the weight of the new person directly without first calculating the original average.

Step-by-Step Solution:
Step 1: Let the original average weight of the 8 persons be A kg.Step 2: Original total weight of the group = 8 * A.Step 3: After replacement, the new average becomes A + 2.5 kg, so the new total weight = 8 * (A + 2.5).Step 4: The new total weight is also equal to original total weight minus 65 kg plus weight of the new person, say W: 8 * A - 65 + W.Step 5: Equate both expressions: 8 * (A + 2.5) = 8 * A - 65 + W.Step 6: Expand left side: 8 * A + 8 * 2.5 = 8 * A - 65 + W.Step 7: Simplify: 8 * 2.5 = -65 + W, so 20 = W - 65.Step 8: Therefore W = 65 + 20 = 85 kg.

Verification / Alternative Check:
The increase in average is 2.5 kg across 8 persons, so the net increase in total weight is 2.5 * 8 = 20 kg. This net increase must come from the new person being heavier than the old one. Since the old person weighed 65 kg, the new person must weigh 65 + 20 = 85 kg. This quick method confirms our detailed algebraic solution.

Why Other Options Are Wrong:
A weight of 70 kg or 75 kg would increase the total weight by only 5 kg or 10 kg, which would increase the average by less than 2.5 kg. A weight of 80 kg would increase the total by 15 kg, giving an average increase of 15 / 8 which is less than 2.5 kg. Only 85 kg produces a total increase of 20 kg and therefore the correct average increase of 2.5 kg.

Common Pitfalls:
Many students mistakenly divide the increase in total weight by 7 instead of 8 or they incorrectly add 2.5 kg directly to 65 kg without considering the number of persons involved. Another mistake is to assume that the total number of persons changes, whereas in this problem the group size remains 8 because one person leaves and another person joins. Keeping track of the group size and using the relation change in total = change in average * number of terms avoids such errors.

Final Answer:
The weight of the new person is 85 kg.