JEE Main Mathematics Question (2026) — Solution

Step-by-step solution

Given the equation: 50 ( 2x 1+3i - y 1-2i ) = 31 + 17i Rationalizing the denominators inside the parentheses: 2x 1+3i = 2x(1-3i) (1+3i)(1-3i) = 2x(1-3i) 1^2 + 3^2 = 2x(1-3i) 10 = x(1-3i) 5 y 1-2i = y(1+2i) (1-2i)(1+2i) = y(1+2i) 1^2 + 2^2 = y(1+2i) 5 Substituting these back into the given equation: 50 ( x(1-3i) 5 - y(1+2i) 5 ) = 31 + 17i 10(x(1-3i) - y(1+2i)) = 31 + 17i 10(x - y) - 10i(3x + 2y) = 31 + 17i Equating the real and imaginary parts on both sides: 10(x - y) = 31 10x - 10y = 31 -10(3x + 2y) = 17 -30x - 20y = 17 Multiplying the first equation by 3 gives: 30x - 30y = 93 Adding this to the second equation: (-30x - 20y) + (30x - 30y) = 17 + 93 -50y = 110 y = - 11 5 Substituting y = - 11 5 into 10x - 10y = 31: 10x - 10 (- 11 5 ) = 31 10x + 22 = 31 10x = 9 x = 9 10 Now, finding the value of 10(x - 3y): 10(x - 3y) = 10x - 30y = 10 ( 9 10 ) - 30 (- 11 5 ) 10(x - 3y) = 9 + 66 = 75 Answer: 75