A car travels from $A$ to $B$ at a speed of $20 km/h$ and returns at a speed of $30 km/h$ . The average speed of the car for the whole journey is

25 km/h

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24 km/h

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50 km/h

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5 km/h

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Solution

The correct option is B $24 km/h$
While going from $A$ to $B$ , let the speed be $V_{1}$ and from $B$ to $A$ the speed be $V_{2}$ .
$V_{1} = 20 k m / h$
$V_{2} = 30 k m / h$
If $d$ be the distance $A B$ . Then we can say:
Time required for $A$ to $B = t_{1} = \frac{d}{V_{1}}$
Time required for $B$ to $A = t_{2} = \frac{d}{V_{2}}$

Average speed, $v = \frac{t o t a l d i s t a n c e}{t o t a l t i m e}$
$v = \frac{d + d}{t_{1} + t_{2}}$
$v = \frac{2 d}{\frac{d}{V_{1}} + \frac{d}{V_{2}}}$
$v = \frac{2 V_{1} V_{2}}{V_{1} + V_{2}}$

$v = \frac{2 \times 20 \times 30}{20 + 30}$
$\Rightarrow v = 24 k m / h$

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