Looking back eight years — Aptitude Question
Looking back eight years: The present ages of two people are in the ratio 3 : 4. Eight years ago they were in the… Answer and worked solution on CodeKairo.
- Topic: Problems on Ages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
The present ages of two people are in the ratio 3 : 4. Eight years ago they were in the ratio 2 : 3. What is the sum of their present ages?
Options
- 42
- 49
- 56
- 63
Show the answer and the worked solution
Correct answer: C. 56
Worked solution
- (3x − 8)/(4x − 8) = 2/3 → 9x − 24 = 8x − 16 → x = 8.
- Ages are 24 and 32; sum = 56.
- Check: sixteen and twenty-four eight years ago, ratio 2 : 3. ✓
Answer: 56.
The idea
Subtract the years from both terms for a past ratio. The question asks for the sum, so remember to add at the end.
Shortcut. Both ratios have a one-part gap, so the part size is unchanged between them: 3x − 8 = 2x → x = 8, and the sum is 7x = 56.
Common trap. 42 looks right because 18 and 24 reduce to exactly 3 : 4, but every option is a multiple of 7 and fits the present ratio; eight years back 42 gives 10 : 16 = 5 : 8, not 2 : 3.