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  4. A boy goes to school from his home at a speed of x km / hr. and comes back at a speed of y km/hr. then the average speed of the boy is :-

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Q. A boy goes to school from his home at a speed of $x\, km / hr$. and comes back at a speed of $y\, km/hr$. then the average speed of the boy is :-

Statistics

Solution:

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