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(C) Let the distance between $A$ and $B$ be $d \, km$.The time taken to go from $A$ to $B$ is $t_1 = \frac{d}{12} \, h$.The time taken to return from

Vedclass · Accepted Answer

$6$

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(C) Let the distance between $A$ and $B$ be $d \, km$.The time taken to go from $A$ to $B$ is $t_1 = \frac{d}{12} \, h$.The time taken to return from $B$ to $A$ is $t_2 = \frac{d}{4} \, h$.Total distance covered $= d + d = 2d \, km$.Total time taken $= t_1 + t_2 = \frac{d}{12} + \frac{d}{4} = \frac{d + 3d}{12} = \frac{4d}{12} = \frac{d}{3} \, h$.Average speed $= \frac{	ext{Total distance}}{	ext{Total time}} = \frac{2d}{d/3} = 2d 	imes \frac{3}{d} = 6 \, km/h$.Alternatively,for two equal distances covered at speeds $v_1$ and $v_2$,the average speed is $\frac{2v_1v_2}{v_1 + v_2} = \frac{2 	imes 12 	imes 4}{12 + 4} = \frac{96}{16} = 6 \, km/h$.

$A$ man goes from $A$ to $B$ at a uniform speed of $12 \, km/h$ and returns with a uniform speed of $4 \, km/h$. His average speed (in $km/h$) for the whole journey is?

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