Chennai Express leaves Hyderabad for Chennai at 14:30 hours, travelling at a constant speed of 60 km/h. On the same day, Charminar Express also leaves Hyderabad for Chennai at 16:30 hours, travelling along the same route at a constant speed of 80 km/h. Assuming both trains continue at these speeds, how far from Hyderabad will the two trains meet each other?

Introduction / Context:
This train problem uses relative motion along the same straight track in the same direction, with one train starting later but travelling faster. We must determine the distance from Hyderabad at which the faster train catches up with the slower train.

Given Data / Assumptions:

• Chennai Express leaves Hyderabad at 14:30 and travels at 60 km/h.
• Charminar Express leaves Hyderabad at 16:30 and travels at 80 km/h.
• Both trains move in the same direction on the same route.
• Speeds are constant and there are no stops.
• We are to find the distance from Hyderabad at the time of meeting.

Concept / Approach:
The slower train gets a head start of 2 hours before the faster one departs. We calculate how far the slower train travels during this head start, then treat the situation as a catch up problem where Charminar Express closes the gap at a relative speed equal to the difference in their speeds. Using distance = speed * time, we get both the catch up time and the distance from Hyderabad.

Step-by-Step Solution:
Let t be the time in hours after 14:30 when the trains meet. Distance travelled by Chennai Express (slow train) in time t is 60t km. Charminar Express starts 2 hours later, so its travel time until the meeting is (t - 2) hours. Distance travelled by Charminar Express is 80(t - 2) km. At the meeting point, both have travelled the same distance from Hyderabad, so 60t = 80(t - 2). Expand: 60t = 80t - 160. Rearrange: 80t - 60t = 160, so 20t = 160. Solve: t = 160 / 20 = 8 hours after 14:30. Distance from Hyderabad at meeting = 60t = 60 * 8 = 480 km.

Verification / Alternative check:
At 14:30 + 8 hours = 22:30, Chennai Express has travelled 480 km. Charminar Express has been moving for 6 hours (from 16:30 to 22:30) at 80 km/h and has also travelled 80 * 6 = 480 km. Thus both trains are at the same point 480 km from Hyderabad, confirming the calculated distance.

Why Other Options Are Wrong:
Distances such as 360 km or 240 km correspond to less travel time and would not allow the faster train to close the initial 120 km lead (2 hours * 60 km/h). Distances like 520 km or 600 km imply more time than needed for the faster train to catch up, which would have happened earlier. Hence, only 480 km satisfies the catch up condition.

Common Pitfalls:
Learners may forget that the faster train does not travel for the full time t, but only for t - 2 hours. Another common mistake is to attempt to use average speed instead of relative speed. Always set up distances from a common reference point and equate them at the meeting time.

Final Answer:
The two trains will meet 480 km away from Hyderabad.