Complex NumbersmediumPYQ · JEE Main · 2 Apr 2026 · Shift 1 (Morning)Free

Complex Equation for 10(x - 3y): Value = 75 | JEE Main 2026

JEE Maths question with a full step-by-step solution.

Question

Let

x

and

y

be real numbers such that

50\left(\dfrac{2x}{1+3i}-\dfrac{y}{1-2i}\right)=31+17i

i=\sqrt{-1}

. Then the value of

10(x-3y)

20

31

35

75

correct

Solution

Step 1: Rationalise each denominator:

\frac{2x}{1+3i}=\frac{2x(1-3i)}{10},\qquad \frac{y}{1-2i}=\frac{y(1+2i)}{5}.

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

Step 2: Simplify:

50\cdot\dfrac{2x(1-3i)}{10}=10x(1-3i)

and

50\cdot\dfrac{y(1+2i)}{5}=10y(1+2i)

10x(1-3i)-10y(1+2i)=31+17i,

\big(10x-10y\big)+\big(-30x-20y\big)i=31+17i.

Step 3: Compare real and imaginary parts:

10(x-y)=31,\qquad -30x-20y=17.

Step 4: From the first,

x-y=3.1

. Solving the two equations gives

x=0.9,\qquad y=-2.2.

Step 5:

10(x-3y)=10\big(0.9-3(-2.2)\big)=10(0.9+6.6)=75.

Correct answer: (4)

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