The average weight of 15 men is decreased by 2 kg when one of them whose…
2022
The average weight of 15 men is decreased by 2 kg when one of them whose weight is 70 kg is replaced by a new man. What is the weight of the new man?
Answer: D. 40 — ConceptWhen one member of a group is replaced and the number of members stays unchanged, the change in the total equals the number of members multiplied by…
- A.
35
- B.
45
- C.
38
- D.
40
Attempted by 2 students.
Show answer & explanation
Correct answer: D
Concept
When one member of a group is replaced and the number of members stays unchanged, the change in the total equals the number of members multiplied by the change in the average.
Using signed changes, the replacement value equals the original value plus the change in the total.
Application
There are 15 members and the average decreases by 2 kg, so the change in the total weight is 15 × (−2) = −30 kg.
Let the new man weigh x kg. Replacing 70 kg by x kg gives x − 70 = −30.
Adding 70 to both sides gives x = 40 kg.
Cross-check
Replacing 70 kg with 40 kg lowers the total by 30 kg, and 30 ÷ 15 = 2 kg per person, which matches the stated decrease. Therefore, the new man weighs 40 kg.