CAT 2020 Slot 1 QA Q4 Time, Speed & Distance

Question 4 of the Quantitative Ability (QA) section, CAT 2020 Slot 1, with CAT's official answer and a worked solution.

A train travelled at one-thirds of its usual speed, and hence reached the destination 30 minutes after the scheduled time. On its return journey, the train initially travelled at its usual speed for 5 minutes but then stopped for 4 minutes for an emergency. The percentage by which the train must now increase its usual speed so as to reach the destination at the scheduled time, is nearest to
  1. A
    58
  2. B
    67
  3. C
    50
  4. D
    61

Answer: (B) 67 Time, Speed & Distance MCQ

Solution

  1. At \(\frac13\) speed the trip takes 3T, so \(3T = T+30\) and the usual time T = 15 min.
  2. Return: 5 min at usual speed covers \(\frac13\) of the route, plus 4 min stopped, so 9 min used and 6 min remain.
  3. The remaining part normally takes 10 min, so the speed must become \(\frac{10}{6}\) times usual: an increase of about 66.7%, nearest 67.

Same concept in other years

See every question on Delay or stoppage on the way: new speed needed to arrive on time.

More Time, Speed & Distance questions from CAT

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