Multiple choice

Two places P and Q are 216 km apart and connected by a straight road. Ramesh travels from P to Q, while Suresh travels from Q to P. Starting at the same time, they meet each other after exactly 1 hour and 20 minutes. If Ramesh reaches Q exactly 36 minutes after Suresh reaches P, what is Ramesh's speed in km per hour?

  1. 64 km/h

  2. 68 km/h

  3. 72 km/h

  4. 82 km/h

  5. a
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C Correct answer
Explanation

Let speeds be R and S. Relative speed = 216 / (4/3) = 162 km/h. So R + S = 162. Time taken by Ramesh = 216/R, by Suresh = 216/S. Given 216/R = 216/S + 36/60. Solving the system yields R = 72.

AI explanation

Let Ramesh's speed be x and Suresh's speed be y; since they meet after 1 hour and 20 minutes (which is 4/3 hours), x plus y equals 216 divided by 4/3, giving x plus y equals 162. The total time of travel for Ramesh is 216/x and for Suresh is 216/y. Since Ramesh takes 36 minutes (0.6 hours) longer, 216/x minus 216/y equals 0.6; substituting y equals 162 minus x and solving gives x equals 72. Ramesh's speed is 72 km/h.

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