The average age of 8 men rises by 2 years when two of them, aged 21 and 23, are replaced by two women. What is the average age of the women?
30 years. The group's total rises by 8 x 2 = 16 years. So the women together are 21 + 23 + 16 = 60 years, an average of 30.
Explain it simply
The group size stays 8, so a rise of 2 in the average means the total went up by 16 years. That extra 16 must come from the swap: the two women together are 16 years older than the two men they replaced. Find the women's total, then halve it.
Example
Question: 8 men; two men (21 and 23) are replaced by two women; the average rises by 2.
- Increase in total = 8 x 2 = 16 years.
- Men removed: 21 + 23 = 44 years.
- Women's total = 44 + 16 = 60 years.
- Women's average = 60 / 2 = 30 years.
General rule for replacement: new member(s) total = old member(s) total + (group size x change in average). If the average falls, the change is negative.
Example of a fall: in a team of 11, a 32-year-old is replaced and the average falls by 1. The newcomer is 32 - 11 = 21.
console.log((21 + 23 + 8 * 2) / 2); // Output: 30
console.log(32 - 11 * 1); // Output: 21What to say in the interview
"The group size doesn't change, so the total rises by 8 times 2, which is 16. The women's combined age is the removed 44 plus 16, which is 60, so their average is 30."
Common mistakes
- Dividing the 16-year rise between the women before adding the men's ages.
- Multiplying the change by 2 (people replaced) instead of 8 (group size).