Ratio and product together — Aptitude Question
Ratio and product together: The ratio of a man's age to his son's is 7 : 3 and the product of their ages is 756. Answer and worked solution on CodeKairo.
- Topic: Problems on Ages
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
The ratio of a man's age to his son's is 7 : 3 and the product of their ages is 756. What will the ratio be after 6 years?
Options
- 3 : 2
- 2 : 1
- 5 : 3
- 11 : 7
Show the answer and the worked solution
Correct answer: B. 2 : 1
Worked solution
- 7x × 3x = 21x² = 756 → x² = 36 → x = 6.
- Ages are 42 and 18.
- After 6 years: 48 and 24, a ratio of 2 : 1.
Answer: 2 : 1.
The idea
The ratio gives the form, the product gives the scale. Note that the ratio changes with time — it must be recomputed, not carried forward.
Shortcut. 756 ÷ 21 = 36, so the multiplier is 6 and the ages are 42 and 18. Six years on they are 48 and 24, and the unchanged gap of 24 equals the son's age: exactly 2 : 1.
Common trap. Adding the 6 years to the ratio terms — (7 + 6) : (3 + 6) = 13 : 9 — treats 7 and 3 as ages and points to 3 : 2, the nearest option; they are parts of x = 6, so the ages are 42 and 18, and 48 and 24 after six years.