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 ?

Solution(By Examveda Team)

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
$$\eqalign{ & {\text{Time}} = \frac{{{\text{Distance }}}}{{{2^{{\text{nd}}}}{\text{Speed }} - {\text{ }}{{\text{1}}^{{\text{st}}}}{\text{Speed}}}} \cr & {\text{Time}} = \frac{{16}}{{12 - 8}} \cr & {\text{Time}} = 4{\text{ hrs}} \cr} $$
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
$$\eqalign{ & {{\text{3}}^{{\text{rd}}}}{\text{ Speed}} = \frac{{{\text{Total Distance}}}}{{{\text{Time}}}} \cr & {{\text{3}}^{{\text{rd}}}}{\text{ Speed}} = \frac{{48}}{5} \cr & {{\text{3}}^{{\text{rd}}}}{\text{ Speed}} = 9.6{\text{ km/hrs}} \cr} $$