Sum over difference — Ratio & Proportion Aptitude Question
Sum over difference: If x/y = 2/3, what is the value of (x + y)/(x − y)? Answer and worked solution on CodeKairo.
- Topic: Ratio & Proportion
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 50 seconds
Question
If x/y = 2/3, what is the value of (x + y)/(x − y)?
Options
- −5
- −1/5
- 1/5
- 5
Show the answer and the worked solution
Correct answer: A. −5
Worked solution
- Take x = 2, y = 3.
- (x + y)/(x − y) = 5/(2 − 3) = 5/(−1) = −5.
Answer: −5.
The idea
Substituting is safe, but keep track of the sign: when the numerator of the ratio is smaller, the difference is negative and so is the answer.
Shortcut. Componendo–dividendo: (x + y)/(x − y) = (2 + 3)/(2 − 3). Since x < y the bottom is negative, so the answer is −5.
Common trap. "5" — taking the difference as 3 − 2 = 1 and dropping the minus sign that x − y carries when x is the smaller.