If a man starts at 7 a.m. at $\frac{5}{4}$ of his usual speed, he reaches office 30 minutes early than usual. So with a new speed at what time he reached his office?

9 a.m.

We have,

Note, we know that if the distance is same then the ratio of speed will be inversely proportional to the ratio of time.

                     old             new

Speed            4                 5

Time              5                 4  ( 1unit early)

1 unit = 30 min

4 units = 120 min or in 2 hours

So with a new speed at 7 + 2 = 9 am he reached his office.