The distance between two cities is 30 kilometres. A man travels from the first city to the second at a speed of 30 kilometres per hour and returns along the same route at a speed of 20 kilometres per hour. What is his average speed for the entire round trip (considering both the onward and the return journeys together)?

Introduction / Context:
Average speed problems are very common in quantitative aptitude and direction or distance based reasoning questions. In many questions the speed of going from one place to another is different from the speed while returning. The key idea is that the average speed is not the simple average of the two speeds when the distances in the two parts of the journey are the same. This question checks whether the learner remembers the correct formula and can carefully compute the total distance and the total time for a complete round trip between two cities.

Given Data / Assumptions:

• The distance between the two cities is 30 kilometres.
• The man travels from City A to City B at 30 kilometres per hour.
• He returns from City B to City A at 20 kilometres per hour.
• The route and distance on both legs of the journey are the same.
• We assume there are no breaks, delays or changes in speed within each leg.

Concept / Approach:
To find average speed over a complete journey, we use the fundamental formula: average speed = total distance travelled / total time taken. When the distance covered in the two parts of the journey is the same but speeds are different, a common shortcut is the harmonic mean: average speed = 2 * x * y / (x + y), where x and y are the speeds. However, it is safer for exam purposes to explicitly calculate total distance and total time and then divide, so that mistakes are less likely.

Step-by-Step Solution:
Step 1: Distance from the first city to the second city is 30 kilometres. Step 2: The same distance is covered again on the way back, so total distance = 30 + 30 = 60 kilometres. Step 3: Time taken to go from City A to City B at 30 kilometres per hour is time = distance / speed = 30 / 30 = 1 hour. Step 4: Time taken to return from City B to City A at 20 kilometres per hour is time = distance / speed = 30 / 20 = 1.5 hours. Step 5: Total time for the round trip = 1 hour + 1.5 hours = 2.5 hours. Step 6: Average speed for the entire journey = total distance / total time = 60 / 2.5. Step 7: Compute 60 / 2.5. Multiply numerator and denominator by 10 to avoid decimals: (60 * 10) / (2.5 * 10) = 600 / 25 = 24 kilometres per hour.

Verification / Alternative check:
We can verify using the harmonic mean shortcut for equal distances: average speed = 2 * x * y / (x + y). Here x = 30 and y = 20. So average speed = 2 * 30 * 20 / (30 + 20) = 1200 / 50 = 24 kilometres per hour. This matches the value obtained from the detailed distance and time calculation. Therefore the computed answer is consistent and correct.

Why Other Options Are Wrong:

• Option A, 25 kilometres per hour, is close but incorrect and may come from rough mental estimation rather than proper calculation.
• Option C, 10 kilometres per hour, is much too low. It may come from confusing speed with time or from incorrect division.
• Option D, 26 kilometres per hour, is another nearby distractor meant to trap those who miscalculate 60 / 2.5.
• Option E, 20 kilometres per hour, is simply one of the given speeds and represents a wrong assumption that average speed equals the slower speed.

Common Pitfalls:
A very common mistake is to take the simple average of the two speeds, that is (30 + 20) / 2 = 25 kilometres per hour. This is incorrect because average speed must always be computed as total distance divided by total time, not the average of the speeds. Another mistake is forgetting that the man travels the same distance twice, so the total distance is 60 kilometres, not 30 kilometres. Some learners also mix up the role of time and speed while dividing, which leads to values such as 10 kilometres per hour or other incorrect numbers. Carefully writing distance, speed and time for each leg prevents these errors.

Final Answer:
The man covers a total distance of 60 kilometres in 2.5 hours, so his average speed for the entire round trip is 24 kilometres per hour.