A) 3 km/hr
B) 4 km/hr
C) - 6 km/hr or 4 km/hr
D) 5 km/hr
Correct Answer: B
Solution :
Let the speed of man be x km/hr and the time taken by him to cover 48 km with speed x be t. According to the question,\[48=x\times t\] ...(1) Also, \[48=(x+2)\,(t-4)\] ....(2) \[\Rightarrow \] \[48=xt-4x+2t-8\] \[\Rightarrow \] \[56=48-4x+2t\] [Using (1)] \[\Rightarrow \] \[8=-4x+2t\] \[\Rightarrow \] \[4=-2x+t\] \[\Rightarrow \] \[4=-2x+\frac{48}{x}\] [Using (1)] \[\Rightarrow \]\[2x=-{{x}^{2}}+24\] \[\Rightarrow \] \[{{x}^{2}}+2x-24=0\] \[\Rightarrow \] \[x=\frac{-2\pm \sqrt{4+96}}{2}=4\] or \[-6\] Since, speed cannot be negative. Required speed is \[4\text{ }km/hr\]
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