Question : A man covers a certain distance by bike. If he covers 25% of the distance at the speed of 25 km/hr, 50% of the distance at the speed of 50 km/hr and the remaining distance at the speed of 12.5 km/hr, find his average speed over the whole journey.
Option 1: 20 km/hr
Option 2: 30 km/hr
Option 3: 25 km/hr
Option 4: 35 km/hr
Correct Answer: 25 km/hr
Solution :
Let the total distance be 100 km.
1st 25% of distance = 25 km
Speed = 25 km/hr
Time = $\frac{\text{distance}}{\text{speed}}= \frac{25}{25}= 1$ hour
2nd 50% of distance = 50 km
Speed = 50 km/hr
Time = $\frac{\text{distance}}{\text{speed}}=\frac{50}{50}= 1$ hour
Remaining distance = 100 – 25 – 50 = 25 km
Speed = 12.5 km/hr
Time = $\frac{\text{distance}}{\text{speed}}=\frac{25}{12.5}= 2$ hours
Total time = 1 + 1 + 2 = 4 hours
Average speed = $\frac{\text{Total distance}}{{\text{Total time}}}=\frac{100}{4}=25$ km/hr
Hence, the correct answer is 25 km/hr.
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