Question

Shyam went from Delhi to Shimla via Chandigarh by car. The distance from Delhi to Chandigarh is $\dfrac{3}{4}$ times the distance from Chandigarh to Shimla. The average speed from Delhi to Chandigarh was one and half times that from Chandigarh to Shimla. If the average speed for the entire journey was 49 km/h. What was the average speed from Chandigarh to Shimla?
A. $39.2km/hr$
B. $63km/hr$
C. $42km/hr$
D. $35km/hr$

Answer 1

Hint: According to the question given in the question we have to find the average speed from Chandigarh to Shimla when Shyam went from Delhi to Shimla via Chandigarh by car. The distance from Delhi to Chandigarh is $\dfrac{3}{4}$ times the distance from Chandigarh to Shimla. The average speed from Delhi to Chandigarh was one and half times that from Chandigarh to Shimla. If the average speed for the entire journey was 49 km/h. First of all we have to let the distance from Chandigarh to Shimla which is equal to x km/h and same as the speed from Chandigarh to Shimla is equal to y km/h. We can also understand it with the help of diagram as given below:

Complete step-by-step answer:
Step 1: First of all we have to let the distance from Chandigarh to Shimla which is equal to x km/h and same as the speed from Chandigarh to Shimla is equal to y km/h.
Now, we have to find the average speed from Delhi to Chandigarh $ = \dfrac{3}{2}ykm/hr$
And the distance from Delhi to Chandigarh$ = \dfrac{3}{4}xkm$
Step 2: Now, we have to find the average speed for entire journey
\[ \Rightarrow \dfrac{{\dfrac{3}{4}x + x}}{{\dfrac{3}{4}x \times \dfrac{2}{3}y + \dfrac{x}{y}}} = \dfrac{{\dfrac{{7x}}{4}}}{{\dfrac{x}{{2y}} + \dfrac{x}{y}}}\]
On finding the L.C.M obtained just above,
\[
   \Rightarrow \dfrac{{7x}}{4} \times \dfrac{{2y}}{{3x}} = \dfrac{{7y}}{6}
 \]
Now, as given
$
   \Rightarrow \dfrac{{7y}}{6} = 49 \\
   \Rightarrow y = \dfrac{{49 \times 6}}{7} \\
   \Rightarrow y = 42km/h
 $

Hence, we have obtained the average speed from Chandigarh to Shimla which is $ = 42km/h$

Note: Speed of a moving object can be obtained by dividing the distance travelled by the moving object by the time it takes to cover that distance.
Distance of a moving object can be obtained by the multiplication of the speed of the moving object by the time it takes.