Multiple choice

ஒரு ரயில் அதன் திசையில் செல்லும் இரு நபர்களை கடக்கிறது. இவர்கள் முறையே மணிக்கு 2 கி.மீ, 4 கி.மீ வேகத்தில் நடக்கின்றனர். இவர்களை ரயில் முறையே 9,10 நொடிகளில் கடக்கிறது. எனில் ரயிலின் நீளம் என்ன? A train crosses two people heading in its direction. They walk at 2 km and 4 km per hour respectively. The train crosses them in 9 and 10 seconds respectively. What is the length of the train?

  1. 55 மீ /55m

  2. 60 மீ /60m

  3. 65 மீ/ 65m

  4. 50 மீ /50m

  5. இவற்றில் ஏதுமில்லை/None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let train length be L and speed be V (m/s). Person 1 speed = 2 km/h = 5/9 m/s. Person 2 speed = 4 km/h = 10/9 m/s. Relative speeds are (V - 5/9) and (V - 10/9). L = (V - 5/9)*9 and L = (V - 10/9)*10. 9V - 5 = 10V - 100/9. V = 100/9 - 5 = 55/9 m/s. L = (55/9 - 5/9)*9 = 50 meters.

AI explanation

Let the length of the train be L and its speed be v. Since the train and the people move in the same direction, the relative speed is the difference in their speeds. We use the formula time = distance / relative speed to get 9 = L / (v - 2) and 10 = L / (v - 4), with speeds in km/h. Converting these times to hours gives L / 9 - L / 10 = 2, meaning L/90 = 2, but a proper relative speed conversion of (5/18) km/h to m/s yields 9 = L / ((v - 2)(5/18)) and 10 = L / ((v - 4)(5/18)). Solving these equations yields v = 22 km/h, and substituting v back into the equation gives L = (22 - 2) * (5/18) * 9 = 50 meters. The length of the train is 50 m.

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