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A train enters into a tunnel $AB$ at $A$ and exits at $B$. A jackal is sitting at $O$ in another by passing tunnel $AOB$, which is connected to $AB$ at $A$ and $B$, where $OA$ is perpendicular to $OB$. A cat is sitting at $P$ inside the tunnel $AB$ making the shortest possible distance between $O$ and $P$, such that $AO=30$ km and $PB=32$ km. When a train before entering into the tunnel $AB$ makes a whistle somewhere before $A$, the jackal and cat run towards $A$ they meet with accident at the entrance $A$. The ratio of speeds of jackal and cat is :

  1. $\frac{2}{3}$
  2. $\frac{4}{3}$
  3. $\frac{5}{3}$
  4. $\frac{3}{2}$
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