Time, Speed and Distance Question 2 - CAT 2021
Two trains A and B were moving in opposite directions, their speeds being in the ratio 5 : 3. The front end of A crossed the rear end of B 46 seconds after the front ends of the trains had crossed each other. It took another 69 seconds for the rear ends of the trains to cross each other. The ratio of length of train A to that of train B is:
Step-by-Step Explanation
Visualize the First Phase (Front of A to Rear of B):
Let the speeds of trains A and B be 5x and 3x, respectively. Since they are moving in opposite directions, their relative speed is:
5x + 3x = 8x
When the front ends cross, the journey begins. For the front end of A to reach and cross the rear end of B, the relative distance covered is exactly equal to the length of train B (Lᴮ).
Lᴮ = Relative Speed × Time₁ = 8x × 46
Visualize the Second Phase (Rear ends clearing each other):
For the two trains to clear each other completely from the very start, the total relative distance they must cover is the sum of both lengths (Lᴬ + Lᴮ).
We know that Lᴮ is covered in the first 46 seconds. The problem states it takes another 69 seconds for the rear ends to cross, meaning the remaining relative distance covered during this second stretch is exactly the length of train A (Lᴬ).
Lᴬ = Relative Speed × Time₂ = 8x × 69
Calculate the Length Ratio:
Lᴬ/Lᴮ = (8x × 69)/(8x × 46) = 69/46 = 3/2
Correct Option: A
💡 FundaMakers Tip:
Avoid setting up long-form coordinate equations for complex train-crossing scenarios. Focus entirely on relative distance intervals. Recognizing that the first time interval corresponds directly to Lᴮ and the subsequent time interval corresponds directly to Lᴬ allows you to find the ratio by simply dividing the two time periods (69/46 = 3/2) in seconds.