Half the age, ten years ago — Aptitude Question
Half the age, ten years ago: Ten years ago, Ram was half as old as Shyam. If their present ages are in the ratio 3… Answer and worked solution on CodeKairo.
- Topic: Problems on Ages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
Ten years ago, Ram was half as old as Shyam. If their present ages are in the ratio 3 : 4, what is the sum of their present ages?
Options
- 30
- 35
- 40
- 45
Show the answer and the worked solution
Correct answer: B. 35
Worked solution
- Ram = 3k, Shyam = 4k.
- Ten years ago: 2(3k − 10) = 4k − 10 → 6k − 20 = 4k − 10 → k = 5.
- Ages are 15 and 20; sum = 35.
- Check: 5 is half of 10. ✓
Answer: 35.
The idea
A present-day ratio gives the variable; the past or future statement gives the equation. Substitute k back before answering — the question may want a sum, not an age.
Shortcut. The sum is 3k + 4k = 7k, and 35 is the only option divisible by 7.
Common trap. Taking the ten years off Ram's age but not Shyam's — 2(3k − 10) = 4k — gives k = 10 and ages of 30 and 40, both of which sit among the options; Shyam was ten years younger too, so 2(3k − 10) = 4k − 10, k = 5 and the sum is 35.