Average speed over a trip with different speeds by distance share: On a journey across Delhi, a taxi travels 60% of the distance at 30 km/h, 20% at 20 km/h, and the remaining 20% at 10 km/h. What is the average speed for the whole journey?

Introduction / Context:
When different speeds apply to different fractions of the distance, the correct average speed is the harmonic-mean-like combination weighted by distance fractions, not the simple arithmetic mean.

Given Data / Assumptions:

• Fractions of distance: 0.6, 0.2, 0.2
• Speeds: 30 km/h, 20 km/h, 10 km/h respectively

Concept / Approach:
If fractions of distance are f1, f2, f3 at speeds v1, v2, v3, then 1 / v_avg = f1 / v1 + f2 / v2 + f3 / v3.

Step-by-Step Solution:
1 / v_avg = 0.6 / 30 + 0.2 / 20 + 0.2 / 10= 0.02 + 0.01 + 0.02 = 0.05v_avg = 1 / 0.05 = 20 km/h

Verification / Alternative check:
Let total distance be 1 unit; compute total time as sum of (fi * distance)/vi and divide distance 1 by total time; it yields 20 km/h.

Why Other Options Are Wrong:
22.5, 24.625, 25, 18 km/h do not satisfy the harmonic sum of times given the stated fractions and speeds.

Common Pitfalls:
Taking the arithmetic mean of speeds or weighting by time instead of distance when the fractions refer to distance parts.

Final Answer:
20 km/hr