Arithmetic

Time, Speed & Distance

Medium

A man traveled from the village to the post-office at the rate of 25 km/hr and walked back at the rate of 4 km/hr. If the whole journey took 5 hours 48 minutes, find the distance of the post-office from the village.

20 km

30 km

50 km

60 km

✅ Correct Option: 1

Let the distance from the village to the post-office be $d$ km.

The distance from village to post-office is the same as the distance from post-office back to village.

Speed going to post-office = 25 km/hr

Speed walking back = 4 km/hr

Total time for both trips = 5 hours 48 minutes

Converting the total time to hours:

5 hours 48 minutes = $5 + \dfrac{48}{60}$ hours

$= 5 + \dfrac{4}{5}$

$= 5 + 0.8$

$= 5.8$ hours

Using Time = Distance ÷ Speed:

Time to go to post-office = $\dfrac{d}{25}$ hours

Time to walk back = $\dfrac{d}{4}$ hours

The total time is 5.8 hours:

$\dfrac{d}{25} + \dfrac{d}{4} = 5.8$

The LCM of 25 and 4 is 100.

$\dfrac{4d}{100} + \dfrac{25d}{100} = 5.8$

$\dfrac{29d}{100} = 5.8$

$29d = 580$

$d = 20$

The distance of the post-office from the village is 20 km.

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Solution

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