A man covers a journey from Meerut to Delhi by car at an average speed of 40 km/h. He returns from Delhi to Meerut by scooter at an average speed of 24 km/h. What is his average speed for the entire round trip?

Introduction:
This is a classic average speed problem for a round trip where the distances are equal but the speeds are different in the two directions. It helps you understand why the average speed is not simply the arithmetic mean of the two speeds.

Given Data / Assumptions:
Speed from Meerut to Delhi = 40 km/h. Speed from Delhi to Meerut = 24 km/h. Distance between Meerut and Delhi is the same in both directions (let it be D km). We need the average speed for the entire journey (going and coming back).

Concept / Approach:
For a round trip with equal distances but different speeds, the average speed is given by the harmonic mean: Average speed = (2 * v1 * v2) / (v1 + v2). Alternatively, you can compute total distance and total time: Total distance = D (going) + D (coming) = 2D. Total time = D / 40 + D / 24. Then average speed = total distance / total time.

Step-by-Step Solution:
Step 1: Use the harmonic mean formula for equal distances. Let v1 = 40 km/h and v2 = 24 km/h. Average speed = (2 * v1 * v2) / (v1 + v2). Average speed = (2 * 40 * 24) / (40 + 24). Compute numerator: 2 * 40 * 24 = 1920. Compute denominator: 40 + 24 = 64. Average speed = 1920 / 64 = 30 km/h.

Verification / Alternative Check:
Assume the distance between the two cities is 120 km for easy numbers. Then: Time going = 120 / 40 = 3 hours. Time coming = 120 / 24 = 5 hours. Total distance = 240 km. Total time = 3 + 5 = 8 hours. Average speed = 240 / 8 = 30 km/h, confirming the result.

Why Other Options Are Wrong:
32 km/h and 31 km/h: These are bigger than the computed average and closer to the higher speed, which would only occur if most of the journey were at the higher speed. 27 km/h and 28 km/h: These are lower than 30 km/h and would mean more time spent at the slower speed than actually occurs.

Common Pitfalls:
A very common mistake is to take the simple average of the two speeds (40 and 24) and write (40 + 24) / 2 = 32 km/h. This is wrong because the time spent at each speed is different. When distances are equal, always use total distance over total time or the harmonic mean formula.

Final Answer:
The average speed for the whole journey is 30 km/h.