Adding 10 to both numbers — Aptitude Question
Adding 10 to both numbers: Two numbers are in the ratio 3 : 5. If 10 is added to each, the ratio becomes 5 : 7. Answer and worked solution on CodeKairo.
- Topic: Ratio & Proportion
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
Two numbers are in the ratio 3 : 5. If 10 is added to each, the ratio becomes 5 : 7. What is the smaller number?
Options
- 9
- 12
- 15
- 18
Show the answer and the worked solution
Correct answer: C. 15
Worked solution
- Let the numbers be 3x and 5x.
- (3x + 10)/(5x + 10) = 5/7 → 21x + 70 = 25x + 50 → 4x = 20 → x = 5.
- The numbers are 15 and 25, so the smaller is 15.
Answer: 15.
The idea
Introduce one variable through the ratio, then cross-multiply the second condition. Always substitute back and check both ratios hold.
Shortcut. Both ratios have a gap of 2 parts and the gap never changes, so a part is the same size in both; adding 10 moved the smaller from 3 parts to 5, so 1 part = 5 and it is 15.
Common trap. "18" — its check, 28 : 40 = 0.70, sits within a whisker of 5 : 7 ≈ 0.714, so a rough decimal test passes it; only 15 gives 25 : 35 = 5 : 7 exactly.