a) 120 kmph
b) 100 kmph
c) 80 kmph
d) 75 kmph
Answer: c
Explanation: P __________100km__________Q
Let car takes time T hours to reach destination.
So, Bike will take $$\left( {{\text{T}} + \frac{{25}}{{60}}} \right)$$
Let speed of the bike = S kmph
Speed of Car = S + 50% of S = $$\frac{{3{\text{S}}}}{2}$$ kmph
For the both the case distance is constant. And when distance remain constant then time is inversely proportional to speed (As ST + D)
$$\eqalign{
& \frac{{ {\frac{{3S}}{2}} }}{{\left( S \right)}} = \frac{{ {T + {\frac{5}{{12}}} } }}{T} \cr
& 3T = 2T + \frac{{10}}{{12}} \cr
& T = \frac{{10}}{{12}}{\text{hours}} \cr
& {\text{Speed}}\,{\text{of}}\,{\text{the}}\,{\text{car}} \cr
& \frac{{3S}}{2} = \frac{{100}}{{ {\frac{{10}}{{12}}} }} \cr
& \frac{{3S}}{2} = 120 \cr
& S = 80\,kmph \cr
& {\text{Speed}}\,{\text{of}}\,{\text{the}}\,{\text{bike}} = 80\,kmph \cr} $$
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