125% of ten years ago — Problems on Ages Aptitude Question
125% of ten years ago: A man's present age is 125% of his age 10 years ago and 83⅓% of his age 10 years hence. Answer and worked solution on CodeKairo.
- Topic: Problems on Ages
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 75 seconds
Question
A man's present age is 125% of his age 10 years ago and 83⅓% of his age 10 years hence. What is his present age?
Options
- 45
- 50
- 55
- 60
Show the answer and the worked solution
Correct answer: B. 50
Worked solution
- Let the present age be a. Then a = 1.25(a − 10) = 1.25a − 12.5, so 0.25a = 12.5 and a = 50.
- Check the second condition: 83⅓% of (50 + 10) = 5/6 × 60 = 50. ✓
Answer: 50.
The idea
When a question gives two conditions for one unknown, the second is a consistency check, not extra work. Convert the awkward percentage 83⅓% to the fraction 5/6.
Shortcut. 125% = 5/4, so present : past = 5 : 4. The one-part gap is 10 years, so the present age is 5 × 10 = 50.
Common trap. 60 — his age 10 years hence, the base of the 83⅓%, given in place of the present age.