If $ x : y = 7 : 3 $, then, $ (x - y) : (x + y) = ? $

Question

Examoogle · Accepted Answer

The correct answer is Option C: 5. Ratio Evaluation: $(x - y) : (x + y)$

Step-by-Step Solution & Concepts:
Key Fact: Ratio Evaluation: $(x - y) : (x + y)$

Given: $x : y = 7 : 3$, which means $\frac{x}{y} = \frac{7}{3}$

Key Formulas: $\frac{x - y}{x + y} = \frac{\frac{x}{y} - 1}{\frac{x}{y} + 1} = \frac{\frac{7}{3} - 1}{\frac{7}{3} + 1} = \frac{4/3}{10/3} = \frac{2}{5}$

Key Points: In homogeneous ratio problems, proportionality constants $k$ cancel out directly.; Option C ($2 : 5$) is the simplified answer.

Steps: Direct Substitution Method: Since the expression is homogeneous of degree 1 in numerator and denominator, we can directly substitute $x = 7$ and $y = 3$: $$x - y = 7 - 3 = 4$$ $$x + y = 7 + 3 = 10$$. Simplifying the Ratio: $$\frac{x - y}{x + y} = \frac{4}{10} = \frac{2}{5}$$ In ratio notation, $(x - y) : (x + y) = 2 : 5$.

Answer: C is correct — $(x - y) : (x + y) = 2 : 5$

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