Question : As part of his journey, a person travels 120 km at 80 km/h, the next 100 km at 40 km/h, and returns to the starting point at 75 km/h. The average speed of the person throughout the journey is:
Option 1: 63.46 km/h
Option 2: 58.74 km/h
Option 3: 68.15 km/h
Option 4: 49.58 km/h
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Correct Answer: 63.46 km/h
Solution : Time taken for the first journey $= \frac{120}{80} = \frac{3}{2}$ hr Time taken for the second journey $= \frac{100}{40} = \frac{5}{2}$ hr Distance covered in first and second journeys = 120 + 100 = 220 km While returning, the time taken $=\frac{220}{75 }= \frac{44}{15}$ hr Total distance = 120 + 100 + 220 = 440 km Total time take $= \frac{3}{2} +\frac{5}{2} + \frac{44}{15}=\frac{104}{15}$ hr The average speed $= \frac{440}{\frac{104}{15}} = 63.46$ km/h Hence, the correct answer is 63.46 km/h.
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