A train leaves Hyderabad at 4:00 A.M. and reaches Vijayawada at 8:00 A.M. the same day. Another train leaves Vijayawada at 6:00 A.M. and reaches Hyderabad at 9:30 A.M the same day. At what time do the two trains cross each other?

Given:

A train leaves Hyderabad at 4:00 A.M. and reaches Vijayawada at 8:00 A.M. the same day. Another train leaves Vijayawada at 6:00 A.M. and reaches Hyderabad at 9:30 A.M the same day.

Formula used:

Let the two trains meet at t hours after 6:00 A.M.

Speed of Train 1 = Distance / Time = D / 4 hours

Speed of Train 2 = Distance / Time = D / 3.5 hours

Relative speed when moving towards each other = (D/4) + (D/3.5)

Calculation:

Distance covered by Train 1 in t hours = (D/4) × (t + 2)

Distance covered by Train 2 in t hours = (D/3.5) × t

Since the total distance covered by both trains is D:

⇒ (D/4) × (t + 2) + (D/3.5) × t = D

⇒ (t + 2)/4 + t/3.5 = 1

⇒ (t + 2)/4 + t/3.5 = 1

⇒ (7(t + 2) + 4t) / 28 = 1

⇒ 7t + 14 + 4t = 28

⇒ 11t + 14 = 28

⇒ 11t = 14

⇒ t = 14 / 11

⇒ t = 1.27 hours

⇒ t ≈ 1 hour 16 minutes

So, the two trains cross each other approximately 1 hour and 16 minutes after 6:00 A.M.

∴ The correct answer is option (4) 6:56 A.M.