If two distinct non-zero real variables x and y are such that (x - y) is proportional to (x + y), then the value of x/y: A. depends on x and y B. depends only on x and not on y C. depends only on y and not on x D. is a constant

GATE 2024 · General Aptitude · Ratio Proportion · medium

Answer: D. is a constant

1. Write the proportionality as an equation: By definition of direct proportionality, (x-y) = k(x+y) where k is the constant of proportionality.
2. Divide by y and substitute t = x/y: Divide both sides by y: (x/y) - 1 = k((x/y) + 1). Setting t = x/y: t - 1 = k(t + 1).
3. Solve for t: t - 1 = kt + k => t - kt = k + 1 => t(1 - k) = 1 + k => t = (1+k)/(1-k). This depends only on k, not on individual values of x or y.