At what time does Shyam overtake Ram ?

First, we need to determine whether Shyam overtakes Ram before or after reaching B. For this, we have to find the time at which Shyam is reaching B, and then we have to check where Ram is at that time. 

Shyam is moving at 10 kmph, and the distance between A and B is 5 km. Thus, he will take {5/10 = 0.5} hours to reach B. He left city A at 9:45 AM, hence he will reach B at 10:15 AM.

Now, we will find Ram's position at 10:15 AM. He is moving at 5 kmph and left City A at 9:00 AM. Thus, he has travelled {5 * 1.25 = 6.25} km uptil 10:15 AM. This means that he is returning to city A from city B. Thus, Shyam will overtake Ram while returning to city A. 

Now, again, we will apply the relative motion concept. The distance between Ram and Shyam is 1.25 km (as Ram is ahead of Shyam). The relative speed will be (10 - 5 = 5) kmph (as they are both moving in the same direction). 

Time taken to overtake = $$\frac{1.25}{5}=\frac{1}{4}\ hours=15$$ minutes. 

Thus, Shyam will overtake Ram at 10:30 AM.