A boy goes to a 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 is given by

A boy goes to a 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 is given by

A
AM
B
GM
C
GM
D
none of these

Solution:

Let the distance between the school and the home

be $s$ km. Then, total time taken in going to and coming from the

school is given by

$t = \frac{s}{x} + \frac{s}{y} \Rightarrow t = (\frac{x + y}{x y}) s \Rightarrow \frac{s}{t} = \frac{x y}{x + y}$

Average speed $= \frac{2 s}{t} = \frac{2 x y}{x + y} =$ H. M. of x and y

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