Multiple choice

A train takes $18$ seconds to pas through a platform $162$ m long a $15$ seconds to pass through another platform $120$ m long. The length of the train (in metres) is

  1. $70$
  2. $80$
  3. $90$
  4. $105$
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C Correct answer
Explanation

Let the train length be L and its speed be v. The two situations give L + 162 = 18v and L + 120 = 15v. Subtracting yields 42 = 3v, so v = 14 m/s and L = 90 m.

AI explanation

Let the train's length be L and its speed be S. Using the formula distance equals speed multiplied by time for the first platform gives L plus 162 equals 18S. For the second platform, L plus 120 equals 15S. Subtracting the second equation from the first yields 42 equals 3S, meaning the speed is 14 m/sec. Substituting this back gives L plus 162 equals 18 multiplied by 14, so L is 252 minus 162, resulting in a train length of 90 metres.

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