Question : On a journey across Kolkata, a taxi averages 50 km/hr for 50% of the distance, 40 km/hr for 40% of it and 20 km/hr for the remaining. The average speed (in km/hr) for the whole journey is:
Option 1: 42 km/hr
Option 2: 40 km/hr
Option 3: 35 km/hr
Option 4: 45 km/hr
Correct Answer: 40 km/hr
Solution :
Let us assume that the total distance travelled is 100 km.
Distance travelled at $50$ km/hr = $50$% of $100$ km = $50$ km
Distance travelled at $40$ km/hr = $40$% of $100$ km = $40$ km
Distance travelled at $20$ km/hr = $10$% of $100$ km = $10$ km
Total time taken = $\frac{\text{Distance travelled at 50 km/hr}}{\text{Speed at 50 km/hr}}
+ \frac{\text{Distance travelled at 40 km/hr}}{\text{Speed at 40 km/hr}}
+ \frac{\text{Distance travelled at 20 km/hr}}{\text{Speed at 20 km/hr}}$
= $\frac{50}{ 50} + \frac{40}{ 40} + \frac{10}{ 20}$
= 2.5 hours
$\therefore$ Average speed = $\frac{\text{Total distance travelled }}{\text{Total time taken}}=\frac{100}{ 2.5}=$ 40 km/hr
Hence, the correct answer is 40 km/hr.
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