Let’s draw the diagram for a better understanding. Let the distance from Chandigarh to Shimla be $x$ km. Then the distance from Delhi to Chandigarh $= \frac{3}{4}x$ km.
DIAGRAM
We know that, $\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total TIme}}$
(OR)
$\text{Speed} = \frac{\text{Distance}}{\text{TIme}}$
Let the average speed from chandigarh to shimla be $y \; \frac{km}{h}.$ Then the average speed from Delhi to Chandigarh $= \frac{3}{2} \; y \; \frac{km}{hr}.$
Now, $\frac{x + \frac{3x}{4}}{\frac{x}{y} + \frac{\frac{3x}{4}}{\frac{3y}{2}} } = 49 $
$ \Rightarrow \frac{\frac{4x+3x}{4}}{\frac{x}{y} + \frac{3x}{4} \times \frac{2}{3y}} = 49$
$ \Rightarrow \frac{\frac{7x}{4}}{\frac{x}{y} + \frac{x}{2y}} = 49$
$ \Rightarrow \frac{\frac{7x}{4}}{\frac{2x+x}{2y}} = 49$
$\Rightarrow \frac{7x}{4} \times \frac{2y}{3x} =49$
$\Rightarrow \frac{7y}{6} =49$
$\Rightarrow \boxed{ y =42 \; \frac{km}{hr}}$
$\therefore$ The average speed from Chandigarh to Shimla $y= 42 \; \frac{km}{hr}.$
Correct Answer $: \text{C} $