To reach point B from point A at 4 pm, Sara will have to travel at an average speed of 18 kmph. She will reach point B at 3 pm if she travels at an average speed of 24 kmph. At what average speed should Sara travels to reach point B at 2 pm ?

Answer: Option A

Difference between time = 1 hour
Distance between point AB = x km
According to the question,
$$\Rightarrow \frac{x}{18}-\frac{x}{24}=1$$
L.C.M. of 18 and 24 = 72
$$\begin{array}{rl}& \Rightarrow \frac{4x-3x}{72}=1\\ & \Rightarrow x=72\text{ km}\end{array}$$
Time taken at 18 km/hr to cover 72 km
$$=\frac{72}{18}=4\text{ hours}$$
∴ Speed to cover 72 km in 2 hours :
$$=\frac{72}{2}=36\text{ km/hr}$$