Q.9 Two trains started at 7AM from the same point. The first train travelled north at a speed of
80km/h and the second train travelled south at a speed of 100 km/h. The time at which they
were 540 km apart is ______ AM.
(A) 9 (B) 10 (C) 11 (D) 11.30
Two Trains Started at 7AM: 80km/h North, 100km/h South – When 540 km Apart?
Two trains start from the same point at 7 AM, moving in opposite directions (north at 80 km/h and south at 100 km/h), so their relative speed is the sum, 180 km/h. To be 540 km apart, the time required is distance divided by relative speed: 540 / 180 = 3 hours, meaning 10 AM. This matches option (B).
🔍 Quick Solution
Relative Speed = 80 + 100 = 180 km/h
Time = Distance ÷ Relative Speed = 540 ÷ 180 = 3 hours = 10 AM
Problem Breakdown
Trains moving oppositely increase separation at a combined rate. Distance covered together equals 540 km, calculated as (80t + 100t) = 540, simplifying to 180t = 540, so t = 3 hours.
Option Analysis
| Option | Time Elapsed | Distance (180 km/h × time) | Status |
|---|---|---|---|
| (A) 9 AM | 2 hours | 360 km | ❌ Too short |
| (B) 10 AM | 3 hours | 540 km | ✅ Exact match |
| (C) 11 AM | 4 hours | 720 km | ❌ Too far |
| (D) 11:30 AM | 4.5 hours | 810 km | ❌ Too far |
Why 10 AM is Correct (Full Calculation)
- First train distance: 80 × 3 = 240 km north
- Second train: 100 × 3 = 300 km south
- Total apart: 240 + 300 = 540 km
Relative Speed Formula Explained
Relative speed for opposite motion is speed1 + speed2 = 80 + 100 = 180 km/h. Time = distance / relative speed = 540 / 180 = 3 hours from 7 AM. This avoids errors like using individual speeds alone.
Exam Tips for Train Problems
- Opposite directions: Add speeds (80 + 100 = 180 km/h)
- Same direction: Subtract speeds (100 – 80 = 20 km/h)
- Practice variation: If same direction, time = 540 ÷ 20 = 27 hours
- Common trap: Forgetting to sum speeds leads to wrong options like 9 AM (360 km)
This classic “two trains 540 km apart” problem tests relative speed concepts essential for quantitative aptitude sections.
