A boy goes from his house to school by bus at a speed of 20 km h^-1 and returns back through the same route at a speed of 30 km h^-1. The average speed of his journey is:

1. 24 km h^-1
2. 25 km h^-1
3. 30 km h^-1
4. 20 km h^-1

24 km h^-1

Reason — Suppose the distance between school and house is D km.

In first part the boy goes to school by bus from home at speed (V₁) = 20 km h^-1.

time taken (t₁) = $\dfrac{\text{distance}}{\text{speed}}$ =$\dfrac{\text{D}}{\text{20}}$

In second part the boy returns from school to home through same route at speed(V₂) = 30 km h^-1.

time taken (t₂) = $\dfrac{\text{distance}}{\text{speed}}$ =$\dfrac{\text{D}}{\text{30}}$

Total distance = D + D = 2D km

Total time taken = $\dfrac{\text{D}}{\text{20}}$ + $\dfrac{\text{D}}{\text{30}}$ = $\dfrac{\text{5D}}{\text{60}}$

Average speed = $\dfrac{\text{total distance travelled}}{\text{total time taken}}$

$\text{Speed} = \dfrac{\text{distance}}{\text{time}} \\[1em] = \dfrac{2D}{\dfrac{5D}{60}} \\[1em] = 2 \times 12 \\[1em] = 24 \text{km h}^{-1}$