Q83 / 150 · MHT CET 2023 (13 May Shift 2) · Mathematics

If $(3 x+2)-(5 y-3) \mathrm{i}$ and $(6 x+3)+(2 y-4) \mathrm{i}$ are conjugates of each other, then the value of $\frac{x-y}{x+y}$ is (where $\mathrm{i}=\sqrt{-1}, x, y \in \mathrm{R}$ )

  • A
    $-1$
  • Correct answer
    B
    0
  • C
    1
  • D
    2

Solution

$(3 x+2)-(5 y-3) \mathrm{i}$ and $(6 x+3)+(2 y-4) \mathrm{i}$ are conjugates of each other. $\Rightarrow 3 x+2=6 x+3$ and $5 y-3=2 y-4$ $\Rightarrow 3 x=-1$ and $3 y=-1$ $\Rightarrow x=-\frac{1}{3}$ and $y=-\frac{1}{3}$ $\therefore \quad \frac{x-y}{x+y}=0$

Hence, the correct answer is option: 'B'.

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