Question : Anil completed a certain journey by car. If he covered 35% of the distance at 70 km/h, 40% of the distance at 80 km/h and the remaining distance at 50 km/h, his average speed (in km/h) for the entire journey is:
Option 1: $66 \frac{1}{6} $km/h
Option 2: $66 \frac{2}{3} $km/h
Option 3: $66 \frac{1}{3} $km/h
Option 4: $66 \frac{4}{3} $km/h
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Correct Answer: $66 \frac{2}{3} $km/h
Solution :
Let the total distance covered be 100 km.
Distance covered in the first case = 35% of 100 = 35 km
Speed in the first case = 70 km/h
Time taken in the first case = $\frac{1}{2}$ hr
Distance covered in the second case = 40% of 100 = 40 km
Speed in the second case = 80 km/h
Time taken in the second case = $\frac{1}{2}$ hr
Distance covered in the third case = 100 – 35 – 40 = 25 km
Speed in the third case = 50 km/h
Time taken in the third case = $\frac{1}{2}$ hr
Average speed = $\frac{\text{Total distance}}{\text{Total time}}$
= $\frac{100}{\frac{1}{2}+\frac{1}{2}+\frac{1}{2}}$
= $\frac{100}{\frac{3}{2}}$
= $\frac{200}{3}$
= $66 \frac{2}{3} $km/h
Hence, the correct answer is $66 \frac{2}{3} $km/h.
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