GATE CS 2024 Set 1 Q2 — General Aptitude

Given that $(x+y)$ is proportional to $(x-y)$, we can express this relationship using a constant of proportionality $k$:

where $k$ is a constant. Since $x$ and $y$ are distinct non-zero real variables ($x \neq y$), we have $x - y \neq 0$, which implies $k \neq 1$.

We can rearrange the equation to find the ratio $\frac{x}{y}$:

Dividing both sides by $y(k-1)$ (since $y \neq 0$ and $k \neq 1$):

Since $k$ is a constant, the expression $\frac{k+1}{k-1}$ is also a constant. Therefore, the value of $\frac{x}{y}$ is a constant.