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CAT 2011 | Question: 7

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Two cars $\text{A}$ and $\text{B}$ start from two points $\text{P}$ and $\text{Q}$ respectively towards each other simultaneously. After travelling some distance, at a point $\text{R}$, car $\text{A}$ develops engine trouble. It continues to travel at $\text{2/3 rd}$ of its usual speed to meet car $\text{B}$ at a point $\text{S}$ where $\text{PR = QS}$. If the engine trouble had occurred after car $\text{A}$ had travelled double the distance it would have met car $\text{B}$ at a point $\text{T}$ where $\text{ST = SQ/9}$. Find the ratio of speeds of $\text{A}$ and $\text{B}$. 

  1. $4:1$
  2. $2:1$
  3. $3:1$
  4. $3:2$
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