SSC Selection Post 2022 PYQ — Question 58

The correct answer is option 2 i.e. ${217 \over 729}$.

​​${1 \over x} - {1 \over y} = 10{1 \over 2} =\frac{21}{2}$

⇒ $\frac{y - x}{xy} = \frac{21}{2}$

⇒ $\frac{-\frac{7}{9}}{xy} = \frac{21}{2}$

⇒ $xy = -\frac{2}{27}$

x² + y² = (x - y)² + 2xy = (7/9)² + 2(-2/27) = 49/81 - 4/27 = 37/81

x³ - y³ = (x - y)(x² + xy + y²)

= (7/9)(37/81 -2/27)

= (7/9)(31/81)

= 217/729