A man cycles at the speed of 8 km/hr and reaches office at 11 am and when he cycles at the speed of 12 km/hr, he reaches office at 9 am. At what speed should he cycle so that he reaches his office at 10 am ?

Answer: Option A

First speed = 8 km/hr
Second speed = 12 km/hr
Starting time will be same in both conditions.
Distance travelled by first speed in 2 hours
Time take by second speed to travel distance 16 km
$$\begin{array}{rl}& \text{Time}=\frac{\text{Distance }}{2^{\text{nd}}\text{Speed }-{\text{1}}^{\text{st}}\text{Speed}}\\ & \text{Time}=\frac{16}{12-8}\\ & \text{Time}=4\text{ hrs}\end{array}$$
Total time taken by second speed = 4 hrs
Total distance = 4 × 12 = 48 km
Starting time to travel at second speed :
= 9 am - 4 hrs = 5 am
Total time taken by third speed to reach the office :
= 10 am - 5 am = 5 hrs
$$\begin{array}{rl}& {\text{3}}^{\text{rd}}\text{ Speed}=\frac{\text{Total Distance}}{\text{Time}}\\ & {\text{3}}^{\text{rd}}\text{ Speed}=\frac{48}{5}\\ & {\text{3}}^{\text{rd}}\text{ Speed}=9.6\text{ km/hrs}\end{array}$$