SSC CHSL 10 Jan 2017 Shift 1 Paper

Three numbers a,b,c are in proportion iff ${\mathit{b}}^2=\mathit{a}\mathit{c}$ where b is the mean proportion and c is the third proportion Mean proportion of two numbers x and y = 8
⇒ $\mathit{x}\mathit{y}={\left(8\right)}^2=64$ ------(i)
Third proportion = 512
⇒ ${\mathit{y}}^2=\mathit{x}\times 512$ ------(ii)
Substituting value of from equation(i) in equation(ii), we get :
⇒ ${\mathit{y}}^2=\frac{64}{\mathit{y}}\times 512$
⇒ ${\mathit{y}}^3={\left(2\right)}^6\times 512$
⇒ $\mathit{y}={\left(2\right)}^{\frac{15}{3}}=2^5=32$
Substituting it in equation(i), ⇒ $\mathit{x}=\frac{64}{32}=2$