Multiple choice

Mohit is travelling on his cycle and has calculated to reach point A by 2 p.m. if he travels at 10 km/hr. He will reach there by 12 noon, if he travels at 15 km/hr. At what speed must he travel to reach point A at 1 p.m.?

  1. 12 km/hr

  2. 10 km/hr

  3. 6 km/hr

  4. 15 km/hr

  5. 24 km/hr
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A Correct answer
Explanation

Let distance be D. Time at 10 km/hr = D/10. Time at 15 km/hr = D/15. Difference = D/10 - D/15 = 2 hours (12 noon to 2 p.m.). D/30 = 2, so D = 60 km. To reach at 1 p.m. (1 hour earlier than 2 p.m.), he needs to travel 60 km in (60/10 - 1) = 5 hours. Speed = 60/5 = 12 km/hr.

AI explanation

Let the distance be D and the usual time be T hours; using the given conditions, D equals 10 multiplied by T and D equals 15 multiplied by (T minus 2). Equating the two expressions gives 10T equals 15T minus 30, meaning T is 6 hours and the distance D is 60 km. To arrive at 1 p.m., which is 1 hour earlier than 2 p.m., he must complete the 60 km trip in 5 hours; using the speed formula, his required speed is 60 divided by 5, equaling 12 km/hr.

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