Time, Speed and Distance Question 1 - CAT 2022
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:
Step-by-Step Explanation
Let the meeting time be t minutes after both trains start.
Train A takes 10 minutes for the entire journey, so its remaining travel time after the meeting is (10 − t) minutes.
Train B takes 9 minutes to finish its journey after the meeting point.
Using the standard post-meeting time relationship:
t = √(t₁ × t₂)
where t₁ is the time taken by Train A after meeting, and t₂ is the time taken by Train B after meeting.
t = √[9(10 − t)]
t² = 9(10 − t)
t² + 9t − 90 = 0
(t + 15)(t − 6) = 0
Since time must be positive, t = 6 minutes.
The total time taken by Train B for the entire journey from Y to X is the time before meeting plus the time after meeting:
Total Time B = 6 + 9 = 15 minutes
Correct Option: B
💡 FundaMakers Tip:
Memorize the relationship t = √(t₁ × t₂) for simultaneous reciprocal journeys. Recognizing that Train A's remaining time is (10 − t) and Train B's is 9 allows you to write out the quadratic equation instantly, avoiding the need to track individual speed variables.