GATE CS 2024 Set 1 — Question 2

MCQ+1 / -0.33EasyRatios, Percentages, Powers, Exponents & LogarithmsQuantitative AptitudeGeneral Aptitude

General Aptitude → Quantitative Aptitude → Ratios, Percentages, Powers, Exponents & Logarithms

Last updated 20 August 2026

Question

If two distinct non-zero real variables

x

and

y

are such that

(x + y)

is proportional to

(x - y)

then the value of

\frac{x}{y}

depends on

xy

depends only on

x

and not on

y

depends only on

y

and not on

x

is a constant

(D) is a constant

Given that

(x + y)

is proportional to

(x - y)

, we can write:

(x + y) = k(x - y)

where

k

is a constant of proportionality.

Rearranging the terms to find the ratio

\frac{x}{y}

x + y = kx - ky

y + ky = kx - x

y(1 + k) = x(k - 1)

\frac{x}{y} = \frac{1 + k}{k - 1}

Since

k

is a constant, the expression

\frac{1 + k}{k - 1}

is also a constant. Therefore, the value of

\frac{x}{y}

is a constant.