Multiple choice

A train X of length L m crosses train Y of length (L + 15) m running in from opposite direction in 11 sec. If the speed of train X is S km/hr and the speed of train Y is (S + 18) km/hr, then train X will cross a tunnel of length 360 m in 30 seconds. What can be found from the given data? (i) Time taken to cover (L + 60) m at the speed of (S + 8) km/hr (ii) Ratio of the time taken to cover distance '(L + 10)' m at the speed of 'S' to time taken to cover distance '(L - 40)' m at the speed of '(S + 28)' km/hr (iii) The speed of train X at which a tunnel of length 300 m is crossed in 10 s (iv) Distance covered in 20 min at the speed of (S + 12) km/h

  1. Only (i) and (ii)

  2. Only (ii) and (iii)

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

  4. (i), (ii), (iii) and (iv)

  5. Only (i) and (iv)
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D Correct answer
Explanation

The given data allows solving for L and S using the two time equations (crossing train Y and crossing the tunnel). Once L and S are known, all listed quantities (i) through (iv) can be calculated.

AI explanation

Using the relative speed formula for two bodies moving in opposite directions, the first condition gives 11 = (L + L + 15) / ((S + S + 18) * (5/18)), which simplifies to L = S + 5. The second condition gives 30 = (L + 360) / (S * (5/18)), which simplifies to L = (25S/3) - 360. Solving these equations yields L = 115 and S = 110. Because unique values for both variables are established, all four items can be evaluated.

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