Five years ago the average age of 4 persons A, B, C and D was 45 years. If…
2023
Five years ago the average age of 4 persons A, B, C and D was 45 years. If another person E is included in the group, then the present average age of all the five persons becomes 49 years. What is the present age of E?
Answer: A. 45 years — ConceptFor n quantities, total = average × n. When every person becomes k years older, the group total increases by n × k; this lets totals from different…
- A.
45 years
- B.
50 years
- C.
43 years
- D.
48 years
Show answer & explanation
Correct answer: A
Concept
For n quantities, total = average × n. When every person becomes k years older, the group total increases by n × k; this lets totals from different times be compared on the same date.
Application
Five years ago, the total age of A, B, C and D was 4 × 45 = 180 years.
Over five years, these four people together gain 4 × 5 = 20 years, so their present total is 180 + 20 = 200 years.
The present total age of all five people is 5 × 49 = 245 years.
Therefore, E’s present age is 245 − 200 = 45 years.
Cross-check
Add E’s age to the present total for A, B, C and D: 200 + 45 = 245 years.
Divide the checked total by 5: 245 ÷ 5 = 49 years, which reproduces the stated present average.
E is 45 years old.