SSC CGL 26 Oct 2014 Shift 2 Paper

$2^{\mathit{x}}=4^{\mathit{y}}=8^{\mathit{z}}$
⇒ $2^{\mathit{x}}={\left(2^2\right)}^{\mathit{y}}$ = ${\left(2^3\right)}^{\mathit{z}}$
⇒ $2^{\mathit{x}}=2^{2\mathit{y}}=2^{3\mathit{z}}$
∴ x = 2 y = 3 z ⇒ x = 3z;
y = $\frac{3}{2}$ z
∴ x y z = 288
⇒ 3z × $\frac{3}{2}$ z × z = 288
⇒ 3z = $\frac{3}{2}$ z × z = 288
⇒ $\frac{9}{2}{\mathit{z}}^3$ = 288
⇒ ${\mathit{z}}^3$ = $\frac{288\times 2}{9}$ = 64
⇒ z = $\sqrt[3]{4\times 4\times 4}$ = 4
∴ x = 3z = 3 × 4 = 12
y = $\frac{3}{2}$ z = $\frac{3}{2}$ × 4 = 6
∴ $\frac{1}{2\mathit{x}}+\frac{1}{4\mathit{y}}+\frac{1}{8\mathit{z}}$
= $\frac{1}{2\times 12}+\frac{1}{6\times 4}$ + $\frac{1}{8\times 4}$
= $\frac{1}{24}+\frac{1}{24}+\frac{1}{32}$
= $\frac{4+4+3}{96}$ = $\frac{11}{96}$