Evaluating an expression from a ratio — Aptitude Question
Evaluating an expression from a ratio: If x : y = 5 : 2, what is (8x + 9y) : (8x + 2y)? Answer and worked solution on CodeKairo.
- Topic: Ratio & Proportion
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
If x : y = 5 : 2, what is (8x + 9y) : (8x + 2y)?
Options
- 22 : 29
- 23 : 22
- 29 : 22
- 31 : 22
Show the answer and the worked solution
Correct answer: C. 29 : 22
Worked solution
- Take x = 5 and y = 2.
- 8x + 9y = 40 + 18 = 58; 8x + 2y = 40 + 4 = 44.
- 58 : 44 = 29 : 22.
Answer: 29 : 22.
The idea
Substitute the ratio terms as actual numbers — any pair in that ratio gives the same answer — then reduce. Algebra with x and y is slower and no more reliable.
Shortcut. The top exceeds the bottom by 7y, so the ratio is above 1: 1 + 7y/(8x + 2y) = 1 + 14/44 = 1 + 7/22, i.e. 29 : 22.
Common trap. "22 : 29" — computing 58 and 44 correctly but writing the ratio upside down.