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A dog at point $A$ goes in pursuit of a fox $30$ $m$ away. The dog makes $2$ $m$ and the fox, $1$ m long leaps. If the dog makes two leaps to the fox’s three, at what distance from $A$ will the dog catch up with the fox ?

  1. $100$ $m$
  2. $110$ $m$
  3. $105$ $m$
  4. $120$ $m$
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Relative speed of the dog, $S_r = \dfrac{(2 \times 2m) – (3 \times 1m)}{t},$ where $t$ is the time for two leaps of the dog.  

$\implies S_r = 1m/t$

So, after every $2$ leaps, the dog covers $1m$ distance to the fox. So, to cover $30\;m$ dog will need to make $2 \times 30 = 60$ leaps which will be $2 \times 60 = 120m$.

Correct option: D.
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