A car covers a distance from Town I to Town II at the speed of 56 km/hr and from Town II to Town I at the speed of 53 km/hr. What is the average speed of the car?

### Concept & Average Speed When a certain distance is traveled at speed $x$ and the exact same distance is traveled at speed $y$, the average speed for the whole journey is given by the harmonic mean of the two speeds. $$Average\ Speed = \frac{2xy}{x + y}$$ ### Step-by-Step Solution * Given speed $x = 56$ km/hr. * Given speed $y = 53$ km/hr. * Apply the formula: * Average Speed = $\frac{2 \times 56 \times 53}{56 + 53}$ * Average Speed = $\frac{5936}{109}$ * Average Speed $\approx 54.458$ km/hr. * Since $54.458$ km/hr does not match any of the provided numerical options exactly, the answer is "None of these". ### Exam Strategy & Shortcut Whenever distances are equal, never just average the two speeds (e.g., $(56+53)/2 = 54.5$). The correct average speed is always slightly less than the simple arithmetic average. Here, $54.5$ is the arithmetic average, so the true average is slightly less. Calculating exactly yields $\approx 54.458$, confirming none of the fixed options are precisely correct. ### Common Pitfall Calculating the simple average of the speeds $\frac{56 + 53}{2} = 54.5$ km/hr, or approximating $54.458$ to $54$ km/hr and choosing option (b). Average speed must be exact unless an approximation is explicitly asked for. ### Final Answer Therefore, the correct answer is **None of these**.