A car covers four successive 8 km distances at speeds of 12 km/hr, 18 km/hr, 24 km/hr and 36 km/hr, respectively. Its average speed (in km/hr) over this distance is:

Correct option is A

Given:

- Distances: 8 km each for four stretches => Total distance = 8 × 4 = 32 km

- Speeds: 12 km/hr, 18 km/hr, 24 km/hr, and 36 km/hr

Formula Used:

​$$- Time = \frac{Distance }{ Speed}\\\ \\- Average \ Speed = \frac{Total \ Distance }{ Total \ Time}$$​​

Solution:

Time for 1st stretch  = $$\frac{8}{12} = \frac{2}{3} \ \text{hr}$$​​

Time for 2nd stretch = $$\frac{8}{18} = \frac{4}{9} \ \text{hr} \\$$​

Time for 3rd stretch = $$\frac{8}{24} = \frac{1}{3} \ \text{hr} \\$$​

Time for 4th stretch = $$\frac{8}{36} = \frac{2}{9} \ \text{hr} \\$$​

Total time = $$\frac{2}{3} + \frac{4}{9} + \frac{1}{3} + \frac{2}{9} = \frac{6 + 4 + 3 + 2}{9} = \frac{15}{9} = \frac{5}{3} \ \text{hr} \\$$​​
Total distance = 32 km 
Average Speed = $$\frac{\text{Total Distance}}{\text{Total Time}} = \frac{32}{5/3} = 32 \times \frac{3}{5} = \frac{96}{5} = 19.2 \ \text{km/hr}$$​​