Multiple choice

A train 'A' travelling at a speed of S km/hr leaves from a station X and another train 'B' travelling at a speed of (S + 30) km/hr leaves the same station X after 10 hours in the same direction. Train A meets train B after 1800 km. Which of the following can be obtained from the above given information? (i) Time taken by train A to cross a platform of length 140 m (ii) Time taken by train B to cross a man moving in the same direction as of train A (iii) Speed of train B (iv) Distance travelled by train B in 5 hours

  1. Only (iii) and (iv)

  2. Only (i), (ii) and (iv)

  3. Only (i), (ii) and (iii)

  4. Only (i) and (iv)

  5. All (i), (ii), (iii) and (iv)
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A Correct answer
Explanation

Train A speed S, Train B speed S+30. Train B leaves 10h later. Train A meets B at 1800km. Time A = 1800/S. Time B = 1800/(S+30). Time A - Time B = 10. 1800/S - 1800/(S+30) = 10. 180/S - 180/(S+30) = 1. 180(30) = S(S+30). S^2 + 30S - 5400 = 0. (S+90)(S-60) = 0. S = 60. Speed B = 90. We know speeds, so we can find (iii) and (iv).

AI explanation

Let the speed of train A be S km/hr, making the speed of train B (S + 30) km/hr. Train A travels for 10 hours before train B leaves, covering 10S km. When train B starts, the distance between them is 1800 - 10S km, and since they meet at 1800 km, the equation is (1800 - 10S) / S = 1800 / (S + 30). Solving this gives S = 60 km/hr, which allows us to determine the speed of train B is 90 km/hr. Knowing train B's speed allows us to calculate the distance it travels in 5 hours, but since the lengths of the trains are unknown, we cannot find the times to cross a platform or a man; therefore, only the speed of train B and its distance travelled in 5 hours can be obtained.

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