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A man travels $35$ km partly at $4$ $kmph$ and partly at $5$ $kmph$. If he covers the former distance at $5$ $kmph$ and the later distance at $4$ $kmph$, he could cover $2$ km more in the same time. The time taken to cover the whole distance at the original rate (in hours) is :

  1. $4\frac{1}{2}$
  2. $7$
  3. $8$
  4. $9$
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Answer is C

Case 1

$4t_{1}+5t_{2}=35$  ------(1)

Case 2

$5t_{1}+4t_{2}=37$  ------(2)

On solving simultaneous equations (1) and (2), we will get t1 = 5hrs and t2 = 3hrs

The time taken to cover the whole distance = t1+t2 = 5+3= 8 hrs

 

 

 

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