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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