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 ?

A. 36 km/hr

B. 28 km/hr

C. 25 km/hr

D. 30 km/hr

Answer: Option A

Solution(By Examveda Team)

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
$$\eqalign{ & \Rightarrow \frac{{4x - 3x}}{{72}} = 1 \cr & \Rightarrow x = 72{\text{ km}} \cr} $$
Time taken at 18 km/hr to cover 72 km
$$ = \frac{{72}}{{18}} = 4{\text{ hours}}$$
∴ Speed to cover 72 km in 2 hours :
$$ = \frac{{72}}{2} = 36{\text{ km/hr}}$$