To find the car that maintained the maximum average speed, we use the formula for average speed:

Average Speed = Distance / Time Taken

Now, let's calculate the average speed for each car:

Car A: Average Speed = $240$ km / $4$ hours = $60$ km/h

Car B: Average Speed = $180$ km / $3$ hours = $60$ km/h

Car C: Average Speed = $200$ km / $5$ hours = $40$ km/h

Car D: Average Speed = $160$ km / $4$ hours = $40$ km/h

Conclusion: Car A and Car B both maintained the same maximum average speed of $60$ km/h. However, since the question asks for the car that maintained the maximum average speed, the answer is either Car A or Car B. If only one option must be chosen, the correct answer is:

A. Car A