CAT 2020 Slot 1 QA Q14 Time, Speed & Distance

Question 14 of the Quantitative Ability (QA) section, CAT 2020 Slot 1, with CAT's official answer and a worked solution.

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. A
    87
  2. B
    82
  3. C
    78
  4. D
    75

Answer: (B) 82 Time, Speed & Distance MCQ

Solution

  1. Train speed v km/h, length L. \(L = (v-2)\cdot90 = (v-4)\cdot100\) (in km/h x s units).
  2. \(90v-180 = 100v-400 \Rightarrow v=22\), so \(L = 20\times\frac{90}{3600} = 0.5\) km.
  3. Time to pass a post \(= \frac{0.5}{22}\) h \(= \frac{1800}{22} \approx 81.8\) s, nearest 82.

Same concept in other years

See every question on Trains crossing: relative speed covers the sum of lengths.

More Time, Speed & Distance questions from CAT

All 48 Time, Speed & Distance questions asked since 2017.