Question : A man goes to a place on a bicycle at a speed of 16 km/h and comes back at a lower speed. If the average speed is 6.4 km/h in total journey, then the return speed (in km/h) is:
Option 1: 10
Option 2: 8
Option 3: 6
Option 4: 4
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Correct Answer: 4
Solution :
Given:
Average speed = 6.4 km/h
Speed while going = $x$ = 16 km/h
Let speed while coming to be $y$ km/h
According to the question:
Average speed = $\frac{2xy}{x+y}$
⇒ 6.4 = $\frac{2×16×y}{16+y}$
⇒ 102.4+6.4$y$ = 32$y$
⇒ 102.4 = 32$y$–6.4$y$
⇒ 102.4 = 25.6$y$
$\therefore y$ = $\frac{102.4}{25.6}$ = 4 km/h
Hence, the correct answer is 4.
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