A student travelled from his residence to his college at the rate of 25 km/hr…
2025
A student travelled from his residence to his college at the rate of 25 km/hr and returned to his residence at the rate of 4 km/hr. To and fro journey of the student took 5 hours and 48 minutes. Find the distance of his college from his residence.
Answer: A. 20 km — ConceptFor a fixed distance d travelled at speed v, the travel time is t = d/v. When the outward and return legs cover the same distance, their times must be…
- A.
20 km
- B.
25 km
- C.
30 km
- D.
25.5 km
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Concept
For a fixed distance d travelled at speed v, the travel time is t = d/v.
When the outward and return legs cover the same distance, their times must be calculated separately and then added.
Application
Let the one-way distance between the residence and the college be d km.
Convert the total time: 5 hours 48 minutes = 5 + 48/60 = 5.8 hours = 29/5 hours.
The outward time is d/25 hours and the return time is d/4 hours.
Therefore, d/25 + d/4 = 29/5. Using denominator 100 gives (4d + 25d)/100 = 29/5.
Thus 29d/100 = 29/5, so d = 20 km.
Cross-check
For 20 km, the outward time is 20/25 = 0.8 hour and the return time is 20/4 = 5 hours. Their sum is 5.8 hours, which is 5 hours 48 minutes.
Result: The college is 20 km from the residence.