CAT 2022 Slot 3 QA Q10 Time, Speed & Distance

Question 10 of the Quantitative Ability (QA) section, CAT 2022 Slot 3, with CAT's official answer and a worked solution.

Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.5 hours if they travel towards each other, but 10.5 hours if they travel in the same direction. If the speed of the slower car is 60 km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards each other, is
  1. A
    150
  2. B
    100
  3. C
    90
  4. D
    120

Answer: (C) 90 Time, Speed & Distance MCQ

Solution

  1. Let speeds be \(u\gt v=60\) and initial gap \(d\). Then \(1.5(u+v)=d=10.5(u-v)\).
  2. So \(u+v=7(u-v)\Rightarrow 3u=4v\Rightarrow u=80\).
  3. Moving towards each other they meet after 1.5 h, so the slower car covers \(60\times1.5=90\) km.

Shortcut. The answer is just \(60\times1.5\); no need to find \(u\).

Same concept in other years

See every question on Meeting time moving towards each other vs. in the same direction.

More Time, Speed & Distance questions from CAT

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