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JEE Main · 2026 · 02 Apr 2026 · Shift 1 · Complex Numbers

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

. Then the value of

10 (x - 3 y)

is :

(A)20
(B)31
(C)35
(D)75✓ Correct

Answer: (D)

Solution

Rationalising,

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

and

\frac{y}{1 - 2 i} = \frac{y ( 1 + 2 i )}{5}

. Hence

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

. Comparing parts,

10 (x - y) = 31

and

10 (- 3 x - 2 y) = 17

, i.e.

x - y = 3.1

and

3 x + 2 y = - 1.7

. Solving these gives

y = - 2.2

and

x = 0.9

, so

10 (x - 3 y) = 10 (0.9 - 3 (- 2.2)) = 10 (7.5) = 75

.

JEE Main · 2026 · 02 Apr 2026 · Shift 1 · Single correct option

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