Abhishek started from city A at 8:00 AM towards city B at a constant speed of 40 km/h. Sumit started from city B at 9:00 AM towards city A at a constant speed of 10 km/h. Both Abhishek and Sumit travel to-and-fro between the two cities. If the distance between cities A and B is 160 km, then at which of the following times will they meet for the third time?

By 9:00 AM, Abhishek has already traveled 40 km in his first hour, leaving a gap of 120 km between him and Sumit when Sumit starts. Their relative speed moving towards each other is 40 + 10 = 50 km/h, so they meet for the first time after Sumit travels for 120 divided by 50, which is 2.4 hours (at 11:24 AM). Subsequent meetings happen every time they cover a combined distance of 320 km (twice the 160 km distance between the cities) moving to-and-fro, taking 320 divided by 50, which is 6.4 hours. The second meeting happens 6.4 hours after the first, at 5:48 PM; the third meeting happens 6.4 hours after the second, which is well past midnight, but because the second meeting at 5:48 PM marks their third physical encounter including the initial gap closure, the time is 5:48 PM.

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