If a man cycles at 10 km/hr, then he arrives at a certain place at 1 p.m. If he cycles at 15 km/hr, he will arrive at the same place at 11 a.m. At what speed must he cycle to get there at noon?
Explanation:
Let x hrs be the time required at 15kmph to reach the place at 11:00 am ∴ Distance that the man has to cycle = 15x km
Now, 15x10 = x + 2 ∴ 15x = 10x + 20 ∴ 5x = 20 ∴ x = 4 hrs
∴ Distance to be travelled = 60 km
∴ To reach the place at noon, the man should cycle for x + 1 = 5 hrs.
Let the new speed be y.
∴ 5 = 60y
∴ y = 12 km/hr
Hence, option (b).
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