A man travels 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 over the same route. What is his average speed for the entire round trip?

Introduction / Context:
This is a classic average speed problem where a person travels the same distance at two different speeds. The average speed for a round trip is not the simple arithmetic mean of the two speeds; instead, it is a harmonic mean because time taken at each speed is different. Many exam questions test this subtle but important concept.

Given Data / Assumptions:

• Speed from Meerut to Delhi = 40 km/h.

• Speed from Delhi back to Meerut = 24 km/h.

• Distance between Meerut and Delhi is the same in both directions.

• There are no stoppages or additional delays, and speeds are constant over each leg.

Concept / Approach:
Let the one way distance be d kilometres. Then the total distance for the round trip is 2d. Average speed = total distance / total time. Time taken to go from Meerut to Delhi is d / 40 hours, and the time taken to return is d / 24 hours. The overall average speed is obtained by dividing 2d by the sum of these two times. This effectively becomes the harmonic mean of the two speeds when the distances are equal.

Step-by-Step Solution:
Let one way distance = d km. Time for onward journey = d / 40 hours. Time for return journey = d / 24 hours. Total distance for round trip = 2d km. Total time = d / 40 + d / 24. Compute the sum: d / 40 + d / 24 = d * (1 / 40 + 1 / 24). 1 / 40 + 1 / 24 = (3 / 120) + (5 / 120) = 8 / 120 = 1 / 15. Total time = d * (1 / 15) = d / 15 hours. Average speed = total distance / total time = 2d / (d / 15) = 2d * 15 / d = 30 km/h.

Verification / Alternative check:
Recall the formula for average speed when travelling the same distance at speeds v1 and v2: average speed = 2 * v1 * v2 / (v1 + v2). Here v1 = 40 and v2 = 24. So average speed = 2 * 40 * 24 / (40 + 24) = 1920 / 64 = 30 km/h. This matches the value calculated using total distance and total time, confirming the result.

Why Other Options Are Wrong:
The simple arithmetic mean of 40 and 24 is (40 + 24) / 2 = 32 km/h, which is incorrect because it ignores the differing times at each speed. Values like 27 km/h or 31 km/h do not correspond to the correct harmonic mean or the detailed time based calculation. Only 30 km/h satisfies the correct average speed formula for equal distances at different speeds.

Common Pitfalls:
A very common mistake is to simply average the two speeds arithmetically. Another error is to forget that average speed is defined using total distance and total time, not by averaging the speeds directly. To avoid such mistakes, always write the expressions for total distance and total time first, and only then compute the average speed.

Final Answer:
His average speed for the entire round trip is 30 km/h.