A) 30 km/h
B) 25 km/h
C) 20 km/h
D) 15 km/h
Correct Answer: C
Solution :
Let the speed of bike\[=x\,\text{km/h}\] \[\therefore \] Time taken to cover 200 km at a speed of x km/h \[=\frac{200}{x}h\] and new speed of bike\[=(x+5)\text{ km/h}\] \[\therefore \] Time taken to cover 200 km at a speed of \[(x+5)\text{ km/h}\] \[=\frac{200}{x+5}h\] By given condition, \[\frac{200}{x}-\frac{200}{x+5}=2\] \[\Rightarrow \] \[\frac{(x+5-x)200}{{{x}^{2}}+5x}=2\] \[\Rightarrow \] \[500={{x}^{2}}+5x\] \[\Rightarrow \] \[{{x}^{2}}+5x-500=0\] \[\Rightarrow \] \[{{x}^{2}}+25x-20x-500=0\] \[\Rightarrow \] \[x(x+25)-20(x+25)=0\] \[\Rightarrow \] \[(x-20)(x+25)=0\] \[\Rightarrow \] \[x=20\,\text{km/h}\] \[(\because \,\,\,x\ne -\,25)\] \[\therefore \] Original speed of a bike\[=20\,\text{km/h}\]
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