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.
Similar Questions
- What is the average of the first 10 prime numbers?
- A fruit seller has 10 kg of apples and 5 kg of grapes. The price of 1 kg of apples is ₹94.50 and that of grapes is ₹105. He sold all the fruits with him. What is the average amount (in ₹) received by the fruit seller?
- The university has 750 faculty (male and female only) out of which the females are 60%. The average height of females is 162 cm and that of males is 168 cm. What is the average height of the faculty (in cm) of the university?
Important Questions from Average
The average height of 20 students of class 8 is 152 cm and the average height of 15 students of class 9 is 168 cm. What is the average height (to the nearest cm) of the students of both classes?
The average of 4, 6, 8, 12 and x is 7 and the average of x, 9, 13, 15 and y is 9. What is the value of 2x - 3y?
The average weight of 20 girls in a school was 52 kg. Two new students of weight 54 kg and 50 kg were admitted. The ratio of this new average to the old one is:
If the average of two numbers is 13 and the square root of their product is 12, then the difference between the numbers is:
If the average of 5 consecutive odd integers in increasing order is 11 , then the average of the last 3 of them is:
