Two cars, a Maruti and a Toyota, start at the same time from points A and B and move towards each other. The Maruti, starting from A, reaches B in 6 hours 20 minutes, and the Toyota, starting from B, reaches A in 4 hours 45 minutes. If the speed of the Maruti is 60 km/h, what is the speed of the Toyota in km/h?

Introduction / Context:
This question combines the ideas of distance, speed, and time for two vehicles traveling towards each other between two fixed points. It checks whether a student can find the distance between the points from one vehicle's data and then use that distance to compute the speed of the other vehicle. Such problems are very typical in aptitude and entrance examinations.

Given Data / Assumptions:

• Maruti starts from point A and reaches point B in 6 hours 20 minutes.
• Toyota starts from point B and reaches point A in 4 hours 45 minutes.
• Speed of the Maruti = 60 km/h.
• Both cars travel along the same straight road between A and B.
• We assume constant speeds for both vehicles.
• We need to find the speed of the Toyota.

Concept / Approach:
The distance between A and B can be found by using the speed and time of the Maruti. Once the distance is known, the same distance can be used with the time taken by the Toyota to reach the other point to find its speed. We must convert mixed hours and minutes to pure hours for correct calculation. The formula used is distance = speed * time and then speed = distance / time.

Step-by-Step Solution:
Time taken by Maruti = 6 hours 20 minutes = 6 + 20 / 60 hours = 6 + 1 / 3 hours = 19 / 3 hours. Speed of Maruti = 60 km/h. Distance AB = speed * time = 60 * (19 / 3) = 20 * 19 = 380 km. Time taken by Toyota = 4 hours 45 minutes = 4 + 45 / 60 hours = 4.75 hours = 19 / 4 hours. Speed of Toyota = distance / time = 380 / (19 / 4) km/h. Speed of Toyota = 380 * 4 / 19 = 80 km/h.

Verification / Alternative check:
We can check the consistency by verifying that Toyota with speed 80 km/h indeed covers the 380 km distance in 4.75 hours. Compute time = 380 / 80 = 4.75 hours, which exactly matches the given time for Toyota. This confirms that the calculation of both distance and speed is correct and that 80 km/h is the correct speed.

Why Other Options Are Wrong:
A speed of 75 km/h or 72 km/h would require more than 4.75 hours to cover 380 km, conflicting with the given data. Speeds of 86 km/h and 90 km/h would result in shorter travel times than 4.75 hours, again contradicting the problem statement. Only 80 km/h produces the correct distance-time relationship for the Toyota car.

Common Pitfalls:
Common mistakes include not converting the time into fractional hours correctly or incorrectly adding or averaging the two times instead of using them separately. Another error is assuming that the two cars meet at the same time rather than using the complete journeys to compute the distance. Careful unit conversion and strict application of distance = speed * time avoid these issues.

Final Answer:
The speed of the Toyota is 80 km/h.