Deepak starts from A at 10.00 am at a speed of 45 km/hr and Sudhir starts from B at the same time at speed of 50 km/hr towards each other. They meet at 10.11 am but keep moving till they reach at ends (Deepak at B & Sudhir at A), then they turn back and keep moving. At what time do they meet again?
Consider S = Sudhir and D = Deepak
Relative speed between S and D = 50 + 45 = 95 km/hr
Time taken to meet = 11 min
Distance between them = 11 * 95 / 60 km = 17.4167 km
After 11 more mins, S will be at A and D will be at B, because they will cover the same relative distance i.e. 17.4167 km from the point of meet.
After 11 more mins, they meet again, because they will cover the same relative distance i.e. 17.4167 km from the ends.
Totally they travel for 11+11 mins more = 22 mins more.
So, they meet again at 10:33.
The Short-Cut solution :
Just use the following formula :
Time of next meet = Starting Time + 3 * (Time of first meet - Starting Time)
So, Time of next meet = 10:00 + 3 * (10:11 - 10:00) = 10:33