Question : Mohan completed a certain journey by car. If he covered 30% of the distance at 90 km/hr, 45% of the distance at 135 km/hr, and the remaining distance at 75 km/hr. His average speed (in km/hr) for the entire journey is:
Option 1: 100
Option 2: 90
Option 3: 105
Option 4: 95
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Correct Answer: 100
Solution : Let the total distance travelled by Mohan = $100x$ km 30% of distance = $30x$ km 45% of distance = $45x$ km Remaining distance = ($100x-30x-45x$) = $25x$ km According to the question, $\therefore$ Total time taken = $\frac{30x}{90}$+$\frac{45x}{135}$+$\frac{25x}{75}$ = $\frac{x}{3}$+$\frac{x}{3}$+$\frac{x}{3}$ = $\frac{3x}{3}$ = $x$ Average speed = $\frac{\text{Total distance travelled}}{\text{Total time taken}}$ = $\frac{100x}{x}$ = 100 km/hr. Hence, the correct answer is 100.
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