CAT 2022 Slot 1 QA Q6 Time, Speed & Distance

Question 6 of the Quantitative Ability (QA) section, CAT 2022 Slot 1, with CAT's official answer and a worked solution.

Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is
  1. A
    15
  2. B
    12
  3. C
    6
  4. D
    10

Answer: (A) 15 Time, Speed & Distance MCQ

Solution

  1. Let the trains meet after \(t\) minutes. A then needs \(10 - t\) more minutes; B needs 9 more minutes.
  2. Standard meeting result: \(t^2 = (\text{A's time after meeting}) \times (\text{B's time after meeting})\), so \(t^2 = 9(10 - t)\).
  3. \(t^2 + 9t - 90 = 0 \Rightarrow (t+15)(t-6) = 0 \Rightarrow t = 6\).
  4. B's total time \(= 6 + 9 = 15\) minutes.

Shortcut. Time to meet is the geometric mean of the two after-meeting times.

Same concept in other years

See every question on After meeting, speed ratio = √(ratio of remaining times).

More Time, Speed & Distance questions from CAT

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