SSC CGL 4 Sep 2016 Paper

The point of intersection of medians of a triangle is called centroid. It divides each median in the ratio 2 : 1.
∴ $\frac{\mathit{A}\mathit{G}}{\mathit{G}\mathit{D}}$ = $\frac{2}{1}$ ⇒ $\frac{\mathit{G}\mathit{D}}{\mathit{A}\mathit{G}}$ = $\frac{1}{2}$
⇒ $\frac{\mathit{G}\mathit{D}}{\mathit{A}\mathit{G}}$ + 1 = $\frac{1}{2}$ + 1
⇒ $\frac{\mathit{G}\mathit{D}+\mathit{A}\mathit{G}}{\mathit{A}\mathit{G}}$ = $\frac{1+2}{2}$
⇒ $\frac{\mathit{A}\mathit{D}}{\mathit{A}\mathit{G}}$ = $\frac{3}{2}$
⇒ AG : AD = 2 : 3