Shankar covers a certain distance by a car driving at 40 km/h and he returns to the starting point riding on a scooter with a speed of 20 km/h. Find the average speed of the whole journey.

The correct option is $26\frac{2}{3}\text{ km/h}$.

Step-by-step explanation:

Let the distance of the forward journey (from starting point to destination) be $d$ km.

Since Shankar returns to the starting point, the distance of the return journey is also $d$ km.

1. Calculate the time taken for the forward journey:

Speed during the forward journey, $v_1=40\text{ km/h}$.

Time taken, $t_1=\frac{\text{Distance}}{\text{Speed}}=\frac{d}{40}$ hours.

2. Calculate the time taken for the return journey:

Speed during the return journey, $v_2=20\text{ km/h}$.

Time taken, $t_2=\frac{\text{Distance}}{\text{Speed}}=\frac{d}{20}$ hours.

3. Calculate the average speed of the whole journey:

Total distance covered = $d+d=2d$ km.

Total time taken = $t_1+t_2=\frac{d}{40}+\frac{d}{20}=\frac{d+2d}{40}=\frac{3d}{40}$ hours.

Using the average speed formula:

$\text{Average Speed}=\frac{\text{Total Distance}}{\text{Total Time}}$

$\text{Average Speed}=\frac{2d}{\frac{3d}{40}}=\frac{2d\times 40}{3d}=\frac{80}{3}\text{ km/h}$

Converting $\frac{80}{3}$ into a mixed fraction:

$80÷3=26$ with a remainder of $2$.

Thus, $\text{Average Speed}=26\frac{2}{3}\text{ km/h}$.