SSC CGL 16 Aug 2015 Shift 1 Paper

5x + 9y = 5
On cubing both sides,
${\left(5\mathit{x}\right)}^3+{\left(9\mathit{y}\right)}^3$ + 3 × 5x × 9y (5x + 9y) = ${\left(5\right)}^3$
[Since ${\left(\mathit{a}+\mathit{b}\right)}^3$ = ${\mathit{a}}^3+{\mathit{b}}^3$ + 3ab (a + b)]
⇒ $125\mathit{x}3+729{\mathit{y}}^3$ + 135xy × 5 = 125
⇒ 120 + 135 × 5xy = 125
⇒ 135 × 5xy = 125 – 120 = 5
⇒ xy = $\frac{5}{135\times 5}$ = $\frac{1}{135}$