CAT 2021 Question Paper | Quant Slot 2

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 5 : 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

Video Explanation

Explanatory Answer

Two trains A and B were moving in opposite directions, their speeds being in the ratio of 5 : 3.
The speed of train A is 5x.
The speed of train B is 3x.
Let's assume length of train A and train B are L_a and L_b
The front end of A crossed the rear end of B 46 seconds after the front ends of the trains had crossed each other.
So, the distance travelled is L_b. For this, the time taken is 46 sec.
Trains took another 69 seconds for the rear ends of the trains to cross each other.
So, the distance travelled is L_a. For this, the time taken is 69 sec.
\\frac{\frac{L_{a}}{5x + 3x}}{\frac{L_{b}}{5x + 3x}}) =\\frac{69}{46})
The relative speed is (5x + 3x), since they are moving opposite to each other.
\\frac{L_{a}}{L_{b}}) = \\frac{3}{2}) 

The answer is '3 : 2'

Choice D is the correct answer.