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.

Answer: Option C

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