Q. Two Athletes run on a circular track at a steady pace so that first completes one round in eight minutes and the second in ten minutes. If they both start from the same spot at 4pm, when will be the first time they return to the start together? Solution Let them return to start together after m rounds of first and n rounds of second. Then time taken by both should be the same. So time taken = 8*n = 10*m Here both m and n should be integers. The general rule or observation for such problems is that 8*n should have 10 as factor and 10*m should have 8 as factor. So, one possible combination is n = 10, m = 8. But for a perfect solution, we take lcm(least common multiple) of both the times and that is the minimum time after which above criterion is satisfied. lcm of 8 and 10 is 40. So, they start together after 40 minutes. That is at 4:40pm. The rounds completed by first = 5 and that by second = 4.