Multiple choice

The ratio of the lengths of trains Ajanta Express and Thalys is 7 : 9. Moreover, the time taken by both trains to cross a pole on the platform is in the ratio 4 : 5. If the speed of Ajanta Express is 70 km/hr, then find the speed of Thalys in m/s.

  1. 40 m/s

  2. 25 m/s

  3. 29 m/s

  4. 20 m/s

  5. 18 m/s
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D Correct answer
Explanation

Let the lengths be 7x and 9x, and the times be 4y and 5y. Speed = length / time. Speed of Ajanta = 7x / 4y = 70 km/hr, so x/y = 40. Speed of Thalys = 9x / 5y = (9/5) * (x/y) = (9/5) * 40 = 72 km/hr. Converting 72 km/hr to m/s gives 72 * (5/18) = 20 m/s.

AI explanation

Let the lengths of Ajanta Express and Thalys be 7x and 9x, and their times to cross the pole be 4t and 5t. Since speed equals distance divided by time, the speed of Ajanta is 7x / 4t and the speed of Thalys is 9x / 5t. The ratio of their speeds is (7x / 4t) divided by (9x / 5t), which simplifies to 35/36. If Ajanta's speed is 70 km/hr, then Thalys's speed is 70 multiplied by 36/35, resulting in 72 km/hr. Converting 72 km/hr to metres per second gives 72 multiplied by 5/18, which is 20 m/s.

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