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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 ?

- $100$ $m$
- $110$ $m$
- $105$ $m$
- $120$ $m$

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Distance per leap of fox=1m

Dog takes 2 leaps and fox takes 3 leaps in the same time

Distance covered by dog in 2 leaps =2×2=4m

Distance covered by fox in 3 leaps =1×3=3m

In two leaps of dog distance reduces by =4m−3m=1m

No of leaps required by dog to cover the gap of 40 m =40×2=80

Distance covered by dog in 80 leaps =2×80=160m

Hence the dog will catch up with the fox at 160 m from A

Answer: 160 m