Amit and Sumit live in the same house and work in different offices located 24 km and 30 km away from their home respectively. They both leave for work at the same time and reach their offices at 9
A.M. On a particular day, they swapped their office locations. Amit had to start 12 minutes earlier than Sumit to reach the new office at the usual time. What is the speed of Amit?

Distance covered by Amit and Sumit = 24 km and 30 km, respectively.
Since, both of them reached their respective places at same time.
Therefore, ratio of speeds of Amit and Sumit = 24:30 = 4:5.
Let the speeds of Amit and Sumit be 4x km/hr and 5x km/hr, respectively.
Time taken by Amit to reach his place on the day of interchange = 30/4x hours.
Time taken by Sumit to reach his place on the day of interchange = 24/5x hours.
ATQ, (30/4x) – (24/5x) = 12/60.
Or, 7.5/x - 4.8/x = 0.2.
Or, 2.7/x = 0.2.
Or, x = 13.5.
So, speed of Amit = 4x = 54 km/hr.
Hence, the correct answer is C.