Question

A boy goes to a school from his home at a speed of $xkm/hr$ and comes back at a speed of $ykm/hr$, then the average speed is given by

• A. $AM$
• B. $GM$
• C. $HM$
• D. None of these

Answer 1

The correct option is C $HM$

Let the distance between the school and the home be $skm$. Then the total time taken in going to and coming from the school is given by
$t=\frac{s}{x}+\frac{s}{y}\Rightarrow t=\left(\frac{x+y}{xy}\right)s\Rightarrow \frac{s}{t}=\frac{xy}{x+y}$
$\therefore$ Average speed $=\frac{2s}{t}=\frac{2xy}{x+y}=\text{H.M. of}x\text{and}y$