Discussion
If two distinct non-zero real variables x and y are such that (x + y) is proportional to (x − y) then the value of \(\dfrac{x}{y}\)
Answer: D
The ratio \(x/y\) is a constant.
Proportionality means \(x + y = k(x - y)\) for some fixed constant k. Collect the terms:
\[ \begin{aligned} x + y &= kx - ky \\ y(1 + k) &= x(k - 1) \\ \frac{x}{y} &= \frac{k + 1}{k - 1} \end{aligned} \]
The right-hand side contains only the constant k, so \(x/y\) takes the same value whatever the individual values of x and y (and \(k \neq 1\), since y is non-zero). It therefore does not depend on \(xy\), on x alone or on y alone.
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