Ram takes 30 minutes to reach office from home by car. One day, due to heavy traffic he drove his car at (4/5)th of original speed for (1/3)rd of total distance and remaining distance at (2/5)th of the original speed. Find out the time taken by Ram on that day?

Let the distance between Ram’s office and home = 150d
Then his original speed = $$\frac{150d}{30}$$ = 5d

Distance that Ram covered at (1/3)rd of original distance = $$\frac{150d}{3}$$ = 50d
(4/5)th of original speed = $$\frac{4}{5} * 5d$$ = 4d
Time taken by Ram to cover this distance = $$\frac{50d}{4d} = 12.5$$minutes

Remaining distance = 150d - 50d = 100d
(2/5)th of original speed = $$\frac{2}{5}*5d$$ = 2d
Time taken by Ram to cover the remaining distance = $$\frac{100d}{2d}$$ = 50 minutes

Hence total time taken by Ram = 12.5 + 50 = 62.5 minutes