SSC CHSL 2021 PYQ — Question 69

The correct answer is option 3 i.e. 19

a² + b² = 25, x² + y² = 17, ax + by = 8 

$(a + b)^2 = a^2 + b^2 + 2ab$

$(a - b)^2 = a^2 + b^2 - 2ab$

$(ax + by)^2 + (ay - bx)^2 = (a^2 + b^2) × ( x^2 + y^2)$

By using the above formulae; 

(ax + by)² + (ay - bx)² = (a² + b²) × ( x² + y²)

⇒ 8² + (ay - bx)² = 25 × 17

⇒  (ay - bx)² = 425 - 64 = 361

⇒ (ay - bx) = √361 = 19