The average age of a group of 12 students is 20 years. If 4 more students join…
2024
The average age of a group of 12 students is 20 years. If 4 more students join the group, the average age increases by 1 year. What is the average age of the new students?
Answer: A. 24 — CONCEPTAn average represents total quantity divided by the number of members. Therefore, total quantity equals average multiplied by the number of members.…
- A.
24
- B.
26
- C.
23
- D.
22
Show answer & explanation
Correct answer: A
CONCEPT
An average represents total quantity divided by the number of members. Therefore, total quantity equals average multiplied by the number of members.
When members join a group, the newcomers’ combined total is the new group total minus the original group total; their average is that difference divided by their count.
APPLICATION
Original total age = 12 × 20 = 240 years.
After 4 students join, the group has 12 + 4 = 16 students.
The new group average is 20 + 1 = 21 years, so its total age is 16 × 21 = 336 years.
The 4 newcomers’ total age is 336 − 240 = 96 years.
Their average age is 96 ÷ 4 = 24 years.
CROSS-CHECK
Adding four students with total age 4 × 24 = 96 to the original total gives 240 + 96 = 336; dividing by 16 gives 21, exactly one year above 20. Hence the new students’ average age is 24 years.