CAT 2020 Quant Question [Slot 1] with Solution 06

Question

Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 seconds, respectively. The time, in seconds, taken by the train to cross an electric post is nearest to

  1. 87
  2. 82
  3. 75
  4. 78
Option: 2
Solution:

Let the length of the train be l and its speed be s. Given \(\frac{l}{{(s - 2) \times \frac{5}{{18}}}} = 90;\frac{l}{{(s - 4) \times \frac{5}{{18}}}} = 100\)

\( \Rightarrow 90(s - 2) \times \frac{5}{{18}} = 100(s - 4) \times \frac{5}{{18}} \Rightarrow s = 22\)

\(\therefore \) Length of the train =500 m.

Hence the required time to cross a lamp post \( = \frac{{500}}{{22 \times \frac{5}{{18}}}}\)

i.e., 81.81 (or) 82 sec.

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