Averages — “A family of 8 has its average weight increase by 1 kg when a 60-kg member is replaced by a newcomer. What is the newcomer’s weight (in kg)?”

Introduction / Context:This is a classic average replacement question. Replacing one person changes the total by the difference between the newcomer’s weight and the outgoing person’s weight; average change times group size equals change in total.

Given Data / Assumptions:

• Group size = 8 persons.
• Outgoing member weight = 60 kg.
• Average increases by 1 kg after replacement.

Concept / Approach:Let old total be T. New total after replacement is T − 60 + x. The new average is (T − 60 + x)/8, which equals old average T/8 plus 1. Solve for x (the newcomer’s weight).

Step-by-Step Solution:

Verification / Alternative check:The average increase (1 kg) across 8 people means the total weight increased by 8 kg. Since the outgoing person had 60 kg, the newcomer must be 60 + 8 = 68 kg.

Why Other Options Are Wrong:61/62/64 or “none” do not produce the required +8 kg change in total needed for a +1 kg average across 8 members.

Common Pitfalls:Forgetting to multiply the average increase by the number of people; adding 1 kg directly to 60 instead of to the total.

Final Answer:68