The average weight of 8 men is increased by 1.5 kg when one of the men, who weighs 65 kg is replaced by a new man. The weight of the new man is

### Concept & Strategy When a member of a group is replaced and the overall average increases, the new member must weigh more than the departing member. Specifically, the new member must weigh enough to match the departed person's weight, *plus* the extra weight required to increase the average of the entire group. $$New\ Value = Replaced\ Value + (Number\ of\ Entities \times Increase\ in\ Average)$$ ### Step-by-Step Solution * **Determine the total weight increase:** The average weight of all 8 men increases by 1.5 kg. $$Total\ Increase = 8 \times 1.5\text{ kg} = 12\text{ kg}$$ * **Calculate the new man's weight:** The new man must cover the 65 kg of the man he replaced, plus the additional 12 kg that raised the group's average. $$New\ Man = 65\text{ kg} + 12\text{ kg}$$ $$New\ Man = 77\text{ kg}$$ ### Exam Strategy & Shortcut Problems involving a 1:1 replacement don't require you to know the original average. Use the direct deviation formula instantly: $\text{New Weight} = \text{Old Weight} + (\text{Total Members} \times \text{Average Change})$. $65 + (8 \times 1.5) = 77$. You can calculate this mentally in seconds. ### Common Pitfall Adding the average increase (1.5 kg) directly to the replaced man's weight ($65 + 1.5 = 66.5$ kg). Remember that the 1.5 kg increase applies to *every single one* of the 8 men, so you must multiply it by the total group size first. ### Final Answer **Therefore, the correct answer is 77 kg.**