Discussion
A man goes to Mumbai from Allahabad at a speed of 40km/h and returns with the speed of 60km/h. What is his average speed during the whole journey?
Answer: B
The average speed is 48 km/h.
The distance is the same each way, so the time spent at the slower speed is longer and the average is not the simple mean. With distance \(d\) each way:
\[ \begin{aligned} \text{time} &= \frac{d}{40} + \frac{d}{60} = \frac{d}{24} \\ \text{average} &= \frac{2d}{d/24} = 48\ \text{km/h} \end{aligned} \]
This is the harmonic mean, \(\frac{2 \times 40 \times 60}{40 + 60} = 48\). The trap is 50 km/h, the simple average of the two speeds; 45 and 52 come from no valid method.
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