The average weight of 10 persons is increased by 3.5 kg, when one of them whose weight is 45.5 kg is replaced by a new man. The weight (in kg) of the new man is ____.
Understanding the Average Weight Change Problem
This problem involves calculating the weight of a new person based on a change in the average weight of a group. We are given the initial number of people, the change in average weight, and the weight of the person who was replaced.
Calculating the Total Weight Increase
When the average weight of a group increases, it means the total weight of the group has increased. The total increase in weight can be calculated by multiplying the number of people in the group by the increase in the average weight.
- Number of persons ($N$) = 10
- Increase in average weight = 3.5 kg
The total increase in the weight of the group is:
Total Increase = Number of persons $ \times $ Increase in average weight
$ \text{Total Increase} = 10 \times 3.5 \, \text{kg} $
$ \text{Total Increase} = 35 \, \text{kg} $
This means the new man's weight is 35 kg more than the person he replaced.
Determining the New Man's Weight
To find the weight of the new man, we add the total increase in weight to the weight of the person who was replaced.
- Weight of the replaced person = 45.5 kg
- Total increase in weight = 35 kg
The weight of the new man is calculated as:
Weight of New Man = Weight of Replaced Person + Total Increase in Weight
$ W_{\text{new}} = W_{\text{old}} + \text{Total Increase} $
$ W_{\text{new}} = 45.5 \, \text{kg} + 35 \, \text{kg} $
$ W_{\text{new}} = 80.5 \, \text{kg} $
Final Answer Summary
The weight of the new man is 80.5 kg. This accounts for the increase of 3.5 kg in the average weight across all 10 people.
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