Let $\mathrm{ABC}$ be a triangle. Let a point $\mathrm{P}$ divide $\mathrm{AB}$ in the ratio $1: 2$ internally and a point $\mathrm{Q}$ divide $\mathrm{BC}$ in the ratio $1: 2$ internally. Let $\mathrm{D}$ be the point of intersection of $\mathrm{AQ}$ and $\mathrm{CP}$. If the area of the triangle $\mathrm{ABC}$ is $\mathrm{k}$ square units then the area of the triangle $\mathrm{BCD}$ in sq. units is

• Correct answer
  A

  $\frac{4 k}{7}$
• B

  $\frac{2 k}{7}$
• C

  $\frac{7 k}{2}$
• D

  $\frac{7 k}{4}$

Hence, the correct answer is option: 'A'.