The respective ratio between the speeds of a bike, a van, and a lorry is 3 : 5 : 2. The speed of the van is 250 percent of the speed of the lorry, and the lorry covers 360 km in 12 hours. What is the average of the speeds of the bike and the van together (in km/h)?

Introduction / Context:
This question again uses speed ratios to connect the speeds of three vehicles, and then asks for the simple average of the speeds of two of them. It reinforces the same style of reasoning as other ratio-based speed problems and is very common in aptitude exams under the time and distance topic.

Given Data / Assumptions:
- Speeds of bike, van, and lorry are in the ratio 3 : 5 : 2.
- The van's speed is 250 percent of the lorry's speed, consistent with the ratio (5 : 2 = 2.5 times).
- The lorry covers 360 km in 12 hours.
- All vehicles travel at constant speeds.
- We need the average (arithmetic mean) of the speeds of the bike and the van in km/h.

Concept / Approach:
First, find the actual speed of the lorry using distance and time. Then, treat the ratio 3 : 5 : 2 as 3k, 5k, and 2k for bike, van, and lorry respectively. Use the lorry's actual speed to find the value of k, and then compute the speeds of the bike and the van. Finally, calculate their average speed as (bike speed + van speed) / 2.

Step-by-Step Solution:
Step 1: Compute the speed of the lorry.Speed of lorry = distance / time = 360 km / 12 h = 30 km/h.Step 2: Let the common ratio factor be k.Bike speed = 3k, van speed = 5k, lorry speed = 2k.Step 3: Since 2k = 30, we have k = 15.Step 4: Compute the actual speeds.Bike speed = 3k = 3 * 15 = 45 km/h.Van speed = 5k = 5 * 15 = 75 km/h.Step 5: Compute the average speed of bike and van.Average speed = (45 + 75) / 2 = 120 / 2 = 60 km/h.

Verification / Alternative check:
The van speed being 75 km/h and the lorry speed being 30 km/h is consistent with the statement that van speed is 250 percent of lorry speed, since 75 / 30 = 2.5, or 250 percent. This confirms that the ratio scaling has been applied correctly. The average of 45 km/h and 75 km/h is clearly 60 km/h, matching the chosen answer.

Why Other Options Are Wrong:
- 62 km/h, 64 km/h, and 63 km/h do not equal the true average of 45 km/h and 75 km/h.
- Each of these values would require different base speeds or ratios and would therefore contradict the given ratio and lorry speed data.

Common Pitfalls:
Some test takers mistakenly try to use weighted averages or combine distances, but the question only asks for the numerical average of two speeds. Another pitfall is misreading the ratio or miscalculating the value of k. Always carefully connect the ratio with the actual speed of one of the vehicles and then scale correctly.

Final Answer:
The average speed of the bike and the van together is 60 km/h.