Question

A scooter rider covers a certain distance at a uniform speed of \(45\text{ km}\) per hour and retraces the same path at a uniform speed of \(55\text{ km}\) per hour to reach the starting point. His average speed during the whole journey is:

• A. \(49.5\text{ km/hr}\)
• B. \(50\text{ km/hr}\)
• C. \(50.5\text{ km/hr}\)
• D. \(51\text{ km/hr}\)

Hint:

Since the harmonic mean of two positive, unequal numbers is always strictly less than their arithmetic mean:
\[ \text{Arithmetic Mean} = \frac{45 + 55}{2} = 50\text{ km/hr} \]
The average speed must be strictly less than 50.
Looking at the options, only \(49.5\text{ km/hr}\) is less than 50, allowing you to identify the correct answer immediately.

Answer 1

The Correct Option is A