Question

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

• A. $\frac{x+y}{2}km/hr$
• B. $\sqrt{xy}km/hr$
• C. $\frac{2xy}{x+y}km/hr$
• D. $\frac{x+y}{2xy}km/hr$

Answer 1

Answer: (C)

Let the distance between home and school $=Skm$ time consumed to reach school from home $=\frac{S}{x}$ hr. time consumed to reach home from school $=S/yhr$.
Average speed $=\frac{\text{ total covered distance }}{\text{ timeconsume to covered total distance }}$
$=\frac{S+S}{\frac{S}{x}+\frac{S}{y}}=\frac{2}{\frac{1}{x}+\frac{1}{y}}=\frac{2xy}{x+y}km/hr$