Rajesh walks around a circular field at the rate of one round per hour while Sumit runs around it at the rate of six rounds per hour. If they start from the same point at 7.40 a.m. in same direction, they shall first meet each other at:

When two objects move in the same direction on a circular path, they meet when the faster object gains one full round on the slower object. The relative speed is the difference between their speeds. Rajesh's speed = 1 round/hour. Sumit's speed = 6 rounds/hour. Relative speed = Sumit's speed - Rajesh's speed = 6 - 1 = 5 rounds/hour. The time taken for Sumit to gain one round on Rajesh (i.e., the time until they first meet) is the time it takes to cover 1 round at the relative speed. Time = Distance / Relative Speed = 1 round / (5 rounds/hour) = 1/5 hour. Convert hours to minutes: (1/5) hour × 60 minutes/hour = 12 minutes. They start at 7.40 a.m. They will meet for the first time after 12 minutes.