A man travelled 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.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 20 km
Time = distance ÷ speed. The man covers the same distance \(d\) each way, so the time going and the time returning add up to the whole journey time.
Whole journey time: 48 min \(=\frac{48}{60}=0.8\) h, so 5 h 48 min \(=5.8\,\mathrm{h}=\frac{29}{5}\,\mathrm{h}\)
Time going at 25 km/h \(\displaystyle =\frac{d}{25}\) h, and time returning at 4 km/h \(\displaystyle =\frac{d}{4}\) h
Adding the two times (LCM 100): \(\displaystyle \frac{d}{25}+\frac{d}{4}=\frac{4d+25d}{100}=\frac{29d}{100}\) h
This sum is the whole journey time: \(\displaystyle \frac{29d}{100}=\frac{29}{5}\), so \(\displaystyle \frac{d}{100}=\frac{1}{5}\) and \(d=20\) km