A ratio that changes with time — Aptitude Question
A ratio that changes with time: The present ages of two people are in the ratio 4 : 5. After 5 years the ratio… Answer and worked solution on CodeKairo.
- Topic: Ratio & Proportion
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
The present ages of two people are in the ratio 4 : 5. After 5 years the ratio becomes 5 : 6. What is the present age of the younger?
Options
- 16
- 20
- 24
- 25
Show the answer and the worked solution
Correct answer: B. 20
Worked solution
- (4x + 5)/(5x + 5) = 5/6 → 24x + 30 = 25x + 25 → x = 5.
- The younger is 4x = 20.
Answer: 20.
The idea
Add the same number of years to both terms and cross-multiply. The difference between the two ages never changes, which is a quick sanity check on the answer.
Shortcut. The age gap is 1 part in both ratios, so a part is the same size before and after; 5 years moved the younger from 4 parts to 5, so 1 part = 5 years and the younger is 20.
Common trap. "25" — the younger's age five years from now (or the elder's today), not the younger's present age.