A) 28
B) 35
C) 42
D) 64
Correct Answer: C
Solution :
[c] Let usual speed of the motorcyclist = x According to question, \[\frac{21}{x}-\,\frac{21}{(x+12)}=\frac{60}{9\times 60}hour\] \[\frac{21x+252-21x}{x\,\,(x+12)}=\frac{1}{9}\] \[\Rightarrow \,\,\,\frac{252}{{{x}^{2}}+12x}=\frac{1}{9}\] \[\Rightarrow \,\,\,{{x}^{2}}+12x=2268\] \[\Rightarrow \,\,\,{{x}^{2}}+12x-\,2268=0\] \[\Rightarrow \,\,\,{{x}^{2}}+54x-\,42x-\,2268=0\] \[\Rightarrow \,\,x\,\,(x+54)-42\,\,(x+54)\] \[\therefore \,\,x-42=0\] \[\therefore \,\,x=42\] \[x+54=0\] \[\therefore \,\,x=-54\] \[\therefore \]Usual speed of motorcyclist=42 km/hr.
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