The vertices of a triangle $\text{ABC}$ are $\text{A}(4,6), \text{B}(1,5)$ and $\text{C}(7,2)$. A line is drawn to intersect sides $\text{AB}$ and $\mathrm{AC}$ at $\mathrm{D}$ and $\mathrm{E}$ respectively such that $\mathrm{AD}: \mathrm{AB}=\mathrm{AE}: \mathrm{AC}=: 4$. Calculate the ratio of area of triangle $\mathrm{ADE}$ and area of triangle $\mathrm{ABC}$.
- $1: 16$
- $16: 1$
- $15: 16$
- $1: 1$
