A group of seven persons has an average weight of $40 ext{ kg}$. One person in the group is replaced by a new person whose weight is $60 ext{ kg}$, and as a result, the average weight of the group increases by $2 ext{ kg}$. What is the weight of the person who was replaced?

Question

A group of seven persons has an average weight of $40 	ext{ kg}$. One person in the group is replaced by a new person whose weight is $60 	ext{ kg}$, and as a result, the average weight of the group increases by $2 	ext{ kg}$. What is the weight of the person who was replaced?

Accepted Answer

**Solution:**

1. Calculate the total initial weight of the group:
   - Average weight = $40 	ext{ kg}$
   - Number of persons = $7$
   - Total initial weight = $40 	imes 7 = 280 	ext{ kg}$

2. After replacing one person with a new person weighing $60 	ext{ kg}$, the average increases by $2 	ext{ kg}$, so the new average is:
   - New average = $40 + 2 = 42 	ext{ kg}$

3. Calculate the total weight after replacement:
   - Total new weight = $42 	imes 7 = 294 	ext{ kg}$

4. Let the weight of the person replaced be $x 	ext{ kg}$.

5. The total weight after replacement can also be expressed as:
   - Total new weight = Total initial weight $- x + 60$
   - $294 = 280 - x + 60$

6. Simplify the equation:
   - $294 = 340 - x$
   - $x = 340 - 294 = 46 	ext{ kg}$

**Answer:** $46 	ext{ kg}$

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