The average weight of 30 persons is increased by 2 kg, when one of them whose…
2022
The average weight of 30 persons is increased by 2 kg, when one of them whose weight is 40 kg, is replaced by a new person. What is the weight of the new person?
Answer: B. 100 kg — ConceptAverage weight equals total weight divided by the number of people. For a fixed group size n, total weight equals n multiplied by the average weight.…
- A.
98 kg
- B.
100 kg
- C.
102 kg
- D.
95 kg
Attempted by 4 students.
Show answer & explanation
Correct answer: B
Concept
Average weight equals total weight divided by the number of people.
For a fixed group size n, total weight equals n multiplied by the average weight. Replacing one member changes the total by incoming weight minus outgoing weight.
Application
The group size remains 30 because one person is replaced by one person.
An average increase of 2 kg for 30 people means the total weight increases by 30 × 2 = 60 kg.
Let the new person weigh x kg. Then x − 40 = 60, so x = 100 kg.
Cross-check
Replacing 40 kg by 100 kg adds 60 kg to the group. Dividing 60 kg by 30 people gives the stated 2 kg increase in average.
Therefore, the new person weighs 100 kg.