Jee Mains

Let x and y be real number such that $50\left(\frac{2 \mathrm{x}}{1+3 \mathrm{i}}-\frac{\mathrm{y}}{1-2 \mathrm{i}}\right)=31+17 \mathrm{i}, \mathrm{i}=\sqrt{-1}$. Then the value of 10(x -3y) is

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  • 22 October, 2026 at 6:00 pm #12270
    UPLIFTJEE
    Keymaster

    Let x and y be real number such that $50\left(\frac{2 \mathrm{x}}{1+3 \mathrm{i}}-\frac{\mathrm{y}}{1-2 \mathrm{i}}\right)=31+17 \mathrm{i}, \mathrm{i}=\sqrt{-1}$. Then the value of 10(x -3y) is
    [JEE MAIN 02 April 2026 S I]
    (A) 20
    (B) 31
    (C) 35
    (D) 75

    22 October, 2026 at 6:00 pm #12271
    UPLIFTJEE
    Keymaster

    Solution

    $50\left(\frac{2 \mathrm{x}(1-3 \mathrm{i})}{10}-\frac{\mathrm{y}(1+2 \mathrm{i})}{5}\right)=31+17 \mathrm{i} \Rightarrow 10 \mathrm{x}-(30 \mathrm{x}) \mathrm{i}-10 \mathrm{y}-20 \mathrm{yi}=31+17 \mathrm{i}$

    \[ \begin{aligned} & 10(x-y)=31 \ldots(1) \text { and }-30 x-20 y=17 \\ & \Rightarrow 30 x-30 y-30 x-20 y=93+17 \Rightarrow y=-\frac{110}{50}=-2.2, x=0.9 \therefore 10(x-3 y)=75 \end{aligned} \]
    22 October, 2026 at 6:00 pm #12272
    UPLIFTJEE
    Keymaster

    Answer

    D

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