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In the figure (not drawn to scale) given below, $\text{P}$ is a point on $\text{AB}$ such that $\text{AP : PB} = 4:3. \;\text{PQ}$ is parallel to $\text{AC}$ and $\text{QD}$ is parallel to $\text{CP.}$ In $\triangle \text{ARC},\measuredangle \text{ARC} = 90^{\circ}$, and in $\triangle \text{PQS}, \measuredangle \text{PSQ} = 90^{\circ}$. The length of $\text{QS}$ is $6$ cms. What is ratio $\text{AP : PD}?$ 

  1. $10:3$
  2. $2:1$
  3. $7:3$
  4. $8:3$


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