A train travels from one station X to another station Y at a rate of $20$ km/hr and returns at the rate of $30$ km/hr. The average speed of the total journey is

25

km/hr

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24

km/hr

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35

km/hr

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40

km/hr

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Solution

The correct option is A $24$ km/hr
[B] Let distance between $X + Y$ be $a$
$(t_{1})$ Time taken from X to Y $= \frac{a}{20}$
$(t_{2})$ time taken from Y to X $= \frac{a}{30}$
$H e n c e, t o t a l t i m e = t_{1} + t = \frac{a}{20} + \frac{a}{30} = \frac{a}{12}$
In going from X to Y and returning, distance $= 2 a$
$H e n c e, a v e r a g e s p e e d = \frac{2 a}{a / 12} = 24 k m / h r$

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