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 one and a half times that from Chandigarh to Shimla If the average speed for the entire journey was 49 km/hr what was the average speed from Chandigarh to Shimla?

• A. 39.2 km/hr
• B. 63 km/hr
• C. 42 km/hr
• D. 35 km/hr

Answer 1

Answer: (C)

42 km/hr

Let the distance from Chandigarh to Shimla be x km and the average speed from Chandigarh to Shimla be y km/hr
Then average speed from Delhi to Chandigarh = $\frac{3}{2}ykm/hr$
Distance from Delhi to Chandigarh = $\frac{3}{4}xcm$ $\therefore$ Average speed for entire journey
$=\frac{\frac{3}{4}x+x}{\frac{3}{4}x\times \frac{2}{3y}+\frac{x}{y}}km/hr$ $=\frac{\frac{7x}{4}}{\frac{x}{2y}+\frac{x}{y}}=\frac{\frac{7x}{4}}{\frac{3x}{2y}}=\frac{7x}{4}\times \frac{2y}{3x}=\frac{7y}{6}$
Given $\frac{7y}{6}=49\Rightarrow y=\frac{49\times 6}{7}=42km/hr$