Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

Step 1: Understand the given information

• Distance between stations A and B = 110 km
• Train 1 starts from A at 7 a.m. with a speed of 20 kmph
• Train 2 starts from B at 8 a.m. with a speed of 25 kmph

Step 2: Calculate the head start of Train 1

Between 7 a.m. and 8 a.m., Train 1 travels for 1 hour at 20 kmph.

Distance covered by Train 1 in 1 hour = 20 km

Step 3: Remaining distance between the trains at 8 a.m.

Remaining distance = 110 - 20 = 90 km

Step 4: Use relative speed to find meeting time

From 8 a.m., both trains are moving towards each other.

Combined speed = 20 kmph + 25 kmph = 45 kmph
Time to meet = Distance / Relative speed = 90 / 45 = 2 hours

Step 5: Add the time to 8 a.m.

8 a.m. + 2 hours = 10 a.m.

Answer: 10:00 a.m.

The two trains will meet at 10:00 a.m..

This is a classic relative speed problem involving two trains starting at different times. The key is to account for the early start of the first train and then apply the concept of relative speed when both are moving towards each other. This approach is commonly tested in aptitude and entrance exams.