If a motorcar travels the first half of a distance at a speed of 30 km/h and the remaining half distance at a speed of 50 km/h, what will be its average speed?

Correct option is A

Given:
Speed for first half of distance = 30 km/h
Speed for second half of distance = 50 km/h
Formula Used:
​$$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}$$​​
Solution:
Let the total distance be 2D.
The car covers the first half of the distance D at 30 km/h and the second half D at 50 km/h.
Time taken for first half of distance = $$\frac D {30}$$​​
Time taken for second half of distance = $$\frac D {50}$$

Average speed = $$\frac{2D}{\frac{D}{30}+\frac{D}{50}} = \frac{2D}{\frac{5D+ 3D}{150}} = \frac{2D}{\frac{8D}{150}}= \frac{300D}{8D} = 37.5 \text{km/hr}$$

​Thus, the average speed of the car is 37.5 km/h.