The speeds of a car, a jeep, and a tractor are in the ratio 3 : 5 : 2. The speed of the jeep is 250 percent of the speed of the tractor, and the tractor covers 360 km in 12 hours. What is the average of the speeds of the car and the jeep together (in km/h)?

Introduction / Context:
This question checks your understanding of speed ratios and how to use them to find actual speeds when one real speed is known. You are also asked to find the simple average of two speeds. Such questions are frequently asked in aptitude exams under the topic of time, speed, and distance, and they help in strengthening ratio and proportion concepts.

Given Data / Assumptions:
- The speeds of the car, jeep, and tractor are in the ratio 3 : 5 : 2.
- The speed of the jeep is 250 percent of the speed of the tractor, which is consistent with the ratio 5 : 2 (since 5/2 = 2.5 = 250 percent).
- The tractor covers 360 km in 12 hours.
- All speeds are assumed to be constant.
- We need the average of the speeds of the car and the jeep in km/h.

Concept / Approach:
First, we find the actual speed of the tractor using distance and time. Then, using the ratio 3 : 5 : 2, we determine the speeds of the car and the jeep. Finally, we compute the simple arithmetic mean of these two speeds. The problem mainly uses proportional reasoning and the basic speed formula speed = distance / time.

Step-by-Step Solution:
Step 1: Compute the speed of the tractor.Speed of tractor = distance / time = 360 km / 12 h = 30 km/h.Step 2: Let the common ratio factor be k.Then speeds are: car = 3k, jeep = 5k, tractor = 2k.Step 3: Since the tractor's speed is 30 km/h, we have 2k = 30, so k = 15.Step 4: Compute actual speeds.Car speed = 3k = 3 * 15 = 45 km/h.Jeep speed = 5k = 5 * 15 = 75 km/h.Step 5: Find the average speed of car and jeep.Average speed = (45 + 75) / 2 = 120 / 2 = 60 km/h.

Verification / Alternative check:
The given statement that the jeep speed is 250 percent of the tractor speed is consistent: tractor speed = 30 km/h, jeep speed = 75 km/h, and 75 / 30 = 2.5, which is 250 percent. This confirms that the ratio and the calculated values are correct. Therefore, the average of 45 km/h and 75 km/h must be 60 km/h, matching our answer.

Why Other Options Are Wrong:
- 50 km/h, 70 km/h, and 80 km/h are simple averages of other wrongly assumed speed pairs and do not correspond to the correct values obtained from the ratio 3 : 5 : 2 with tractor speed 30 km/h.
- Only 60 km/h is consistent with the ratio and the actual speeds derived from the given data.

Common Pitfalls:
Some candidates confuse the simple average speed of two different vehicles with weighted averages or harmonic means. Here, the question clearly asks for the average of two speeds, not the average speed over some combined journey. Another common error is to misinterpret percentage statements or to ignore the ratio information when real data is given. Always use both the ratio and the actual numerical data to find the scaling factor correctly.

Final Answer:
The average of the speeds of the car and the jeep is 60 km/h.