A train leaves Station A at 6:00 AM and travels towards Station B at a constant speed of 60 km/h. Another train leaves Station B at 8:00 AM and travels towards Station A at a constant speed of 90 km/h. The distance between the two stations is 540 km. At what time will the two trains meet?

Correct — B. The first train runs alone for 2 hours, so remove that stretch before using the combined speed.

Head start, 6:00 to 8:00 AM: 60 × 2 = 120 km
Gap left at 8:00 AM: 540 − 120 = 420 km

Closing speed, towards each other: 60 + 90 = 150 km/h
Time to close the gap: 420 ÷ 150 = 2.8 h = 2 h 48 min

Meeting time: 8:00 AM + 2 h 48 min = 10:48 AM → option (b)

Why the others are wrong

• (a)
  9:48 AM — 9:48 AM is an hour too early. By then the trains have closed 120 + 150 × 1.8 = 390 km together, so 150 km still separates them.
• (c)
  11:45 AM — By 11:45 AM the trains have run 345 + 337.5 = 682.5 km together, more than the 540 km between the stations, so they met before that.
• (d)
  12:45 PM — By 12:45 PM the trains have run 405 + 427.5 = 832.5 km together, far beyond the 540 km gap, so this is long after they met.

Two trains moving towards each other close the gap at the sum of their speeds, but only while both are moving.

When one starts later, let the early train run alone first and subtract its distance from the gap. Apply the summed speed to what remains, and add the result to the later start time, because that is when the summed speed begins.

Key facts

• Relative speed of two bodies moving towards each other = sum of their speeds, here 60 + 90 = 150 km/h.
• 0.8 hour = 0.8 × 60 = 48 minutes.
• Check: at 10:48 AM the first train has run 4.8 h × 60 = 288 km and the second 2.8 h × 90 = 252 km, and 288 + 252 = 540 km.

Common traps

• Dividing the full 540 km by 150 km/h: that ignores the first train's 2-hour head start and gives 3.6 h.
• Reading 2.8 h as 2 h 8 min or 2 h 80 min: the decimal is a fraction of an hour, and 0.8 h = 48 min.

No directly related past PYQ was found.