[6 km] A man goes to his office from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If

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A man goes to his office from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming, what is the distance between his house and office?

3 km

4 km

5 km

6 km

Explanation:

If a car covers a certain distance at x kmph and an equal distance at y kmph,

the average speed of the whole journey = $\dfrac{2xy}{x+y}$kmph

Hence, average speed = $\dfrac{2 \times 3 \times 2}{2 + 3} = \dfrac{12}{5}$km/hr

Total time taken = 5hours

$\Rightarrow$ Distance travelled = $\dfrac{12}{5} \times 5 $= 12km

$\Rightarrow$ Distance between his house and office =$\dfrac{12}{2}$= 6km

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