An express A starts at 2.30 pm from Nampali station and travels towards Vizag…
2023
An express A starts at 2.30 pm from Nampali station and travels towards Vizag station at speed of 80 kmph. Another express starts at 4.30 pm from Nampali station to Vizag station at speed of 100 kmph. How far away from station Nampali will the two trains meet?
- A.
550 km
- B.
600 km
- C.
700 km
- D.
800 km
Attempted by 8 students.
Show answer & explanation
Correct answer: D
Solution:
Let the first train travel for t hours after 2:30 pm until the meeting point.
The second train starts 2 hours later, so it travels for (t − 2) hours by the meeting time.
Equate distances: speed × time for both trains gives 80·t = 100·(t − 2).
Solve: 80t = 100t − 200 → 20t = 200 → t = 10 hours.
Distance from Nampali = speed of the first train × t = 80 × 10 = 800 km.
Alternative (relative speed) method:
By 4:30 pm the first train is 80 × 2 = 160 km ahead.
Relative speed = 100 − 80 = 20 km/h, so time to catch up = 160 / 20 = 8 hours after 4:30 pm.
Distance from Nampali = distance covered by either train at meeting: 100 × 8 = 800 km (or 80 × 10 = 800 km).