Let x and y be real number such that 50 (frac 2 x 1 + 3 i -frac y 1 - 2 i ) = 31 + 17 i , i = √(-1) . value of 10( x - 3 y ) is :

Mathematics · Complex Numbers

JEE Main 2026 — 2 April, Morning Shift — Question 21

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

Option A:
20
Option B:
31
Option C:
35
Option D:
75
Correct

Answer: D

Step-by-step solution

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

\left.\begin{array}{r} 10(x-y)=31 \\ -30 x-20 y=17 \end{array}\right\}

$30 \mathrm{x}-30 \mathrm{y}=93$ $-10(3 x+2 y)=17$ $\mathrm{x}=0.9, \mathrm{y}=-2.2$ $10(\mathrm{x}-3 \mathrm{y})=75$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 2 April, Morning Shift
Subject: Mathematics
Chapter: Complex Numbers
Topic: Introduction to Complex Numbers