Dilip is on the way to his friend's home and wishes to meet him at 3 pm. If he rides the cycle at a speed of 12 kmph, he will get there at 4 pm. If he rides the cycle at a speed of 18 kmph, he is expected to reach at 2 pm. At what speed should he ride the cycle in order to meet his friend at the desired time?

Let the distance to his friend's home be D km and his target travel time be T hours. From the given conditions, D/12 = T + 1 and D/18 = T - 1. Solving these simultaneous equations yields D = 72 km and T = 5 hours. To meet his friend at exactly 3 pm, he must ride at a speed of 72 divided by 5, which equals 14.4 kmph.

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