Question : Vikas covered a certain distance by bike. If he covers 40% of the distance at 40 km/hr, 50% of the distance at 25 km/hr and the remaining 10% distance at 10 km/hr. Find his average speed over the whole distance.
Option 1: 25 km/hr
Option 2: 28 km/hr
Option 3: 26 km/hr
Option 4: 30 km/hr
Correct Answer: 25 km/hr
Solution :
Given, Vikas covers 40% of the distance at 40 km/hr, 50% of the distance at 25 km/hr, and the remaining 10% distance at 10 km/hr.
Let the total distance be $100x$
We know the average speed
= $\frac{\text{Total distance}}{\text{Sum of total speed}}$
= $\frac{100x}{\frac{100x\times40\%}{40}+\frac{100x\times50\%}{25}+\frac{100x\times10\%}{10}}$
= $\frac{100x}{\frac{100x\times40}{40\times 100}+\frac{100x\times50}{25\times 100}+\frac{100x\times10}{10\times 100}}$
= $\frac{100x}{x+2x+x}$
= $\frac{100x}{4x}$
= $25$ km/hr
Hence, the correct answer is 25 km/hr.
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