Question

Shyam went from Delhi to Shimla via Chandigarh by car. The distance from Delhi to Chandigarh is $\frac{3}{4}$ times the distance from Chandigarh to Shimla. The average speed from Delhi to Chandigarh was half as much again as that from Chandigarh to Shimla. If the average speed for the entire journey was 49 kmph, what was the average speed from Chandigarh to Shimla?

• A. 39.2 kmph
• B. 63 kmph
• C. 42 kmph
• D. None of these

Hint:

When dealing with “half as much again” phrases, interpret it as $1.5 \times$ the base value. Always check average speed using total distance divided by total time.

Answer 1

The Correct Option is B

Let the distance from Chandigarh to Shimla be $d$ km.
Then, the distance from Delhi to Chandigarh = $\frac{3}{4}d$ km.
Let the average speed from Chandigarh to Shimla = $x$ kmph.
From Delhi to Chandigarh, the average speed was half as much again as that from Chandigarh to Shimla. “Half as much again” means $x + \frac{x}{2} = \frac{3x}{2}$.
Time from Delhi to Chandigarh = $\frac{\frac{3}{4}d}{\frac{3x}{2}} = \frac{\frac{3}{4}d}{\frac{3x}{2}} = \frac{d}{2x}$.
Time from Chandigarh to Shimla = $\frac{d}{x}$.
Total distance = $\frac{3}{4}d + d = \frac{7}{4}d$.
Total time = $\frac{d}{2x} + \frac{d}{x} = \frac{d}{2x} + \frac{2d}{2x} = \frac{3d}{2x}$.
Average speed for entire journey = $\frac{\text{Total distance}}{\text{Total time}} = \frac{\frac{7}{4}d}{\frac{3d}{2x}} = \frac{7}{4} \times \frac{2x}{3} = \frac{7x}{6}$.
We are given that average speed for the journey = $49$ kmph.
So: $\frac{7x}{6} = 49 \Rightarrow 7x = 294 \Rightarrow x = 42$. Wait — this matches option (C), not (B). Let’s re-check the speed interpretation.
If Delhi–Chandigarh speed is “half as much again” as Chandigarh–Shimla, then: Speed$_{DC}$ = $x + \frac{1}{2}x = 1.5x$. Yes, that’s correct. So the earlier result $x=42$ kmph is correct.
Thus, the correct answer is $\boxed{42 \ \text{kmph}}$ which matches option (C). The answer key in (B) must be an error if provided.