A car travels 50% faster than a bike. Both start at the same time from A to B. The car reaches 25 minutes earlier than the bike. If the distance from A to B is 100 km, find the speed of the bike.

Solution (By Examveda Team)

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)
So,
$$\eqalign{ & \frac{{ {\frac{{3S}}{2}} }}{{\left( S \right)}} = \frac{{ {T + {\frac{5}{{12}}} } }}{T} \cr & 3T = 2T + \frac{{10}}{{12}} \cr & T = \frac{{10}}{{12}}{\text{hours}} \cr & {\text{Speed}}\,{\text{of}}\,{\text{the}}\,{\text{car}} \cr & \frac{{3S}}{2} = \frac{{100}}{{ {\frac{{10}}{{12}}} }} \cr & \frac{{3S}}{2} = 120 \cr & S = 80\,kmph \cr & {\text{Speed}}\,{\text{of}}\,{\text{the}}\,{\text{bike}} = 80\,kmph \cr} $$