Computer Sciences > Gate 2024 Set-1 > Quants
If two distinct non-zero real variables π‘₯ and 𝑦 are such that (π‘₯ + 𝑦) is proportional to (π‘₯ βˆ’ 𝑦) then the value of (π‘₯/𝑦)
A
depends on π‘₯𝑦
B
depends only on π‘₯ and not on 𝑦
C
depends only on 𝑦 and not on π‘₯
D
is a constant

Correct : d

If (x + y) is proportional to (x βˆ’ y), then:
x + y = k(x βˆ’ y)

Solving:
x + y = kx βˆ’ ky
x βˆ’ kx = βˆ’ky βˆ’ y
x(1 βˆ’ k) = βˆ’y(k + 1)

So,
x/y = (k + 1) / (k βˆ’ 1)

This value depends only on the constant k, not on x or y.

Therefore, x/y is a constant.

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