Question : Sohan makes four journeys of equal distance. In the first journey, his speed was 240 km/hr and in each subsequent journey his speed was half the speed of the previous journey. What is the average speed of Sohan in these four journeys?
Option 1: 50 km/hr
Option 2: 64 km/hr
Option 3: 60 km/hr
Option 4: 52 km/hr
Correct Answer: 64 km/hr
Solution :
Let the distance of each trip be $d$.
For the first trip,
speed = 240 km/hr
$\therefore$ time = $\frac{d}{240}$
For the second trip,
speed = $\frac{240}{2}$ = 120 km/hr
$\therefore$ time = $\frac{d}{120}$
For the third trip,
speed = $\frac{120}{2}$ = 60 km/hr
$\therefore$ time = $\frac{d}{60}$
For the fourth trip,
speed = $\frac{60}{2}$ = 30 km/hr
$\therefore$ time = $\frac{d}{30}$
Average speed = $\frac{\text{total distance}}{\text{total time}}$
= $\frac{d+d+d+d}{\frac{d}{240}+\frac{d}{120}+\frac{d}{60}+\frac{d}{30}}$
= $\frac{4d}{\frac{15d}{240}}$
= $\frac{960}{15}$
= 64 km/hr
Hence, the correct answer is 64 km/hr.
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