Question

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

• A. 2 : 3
• B. 2 : 1
• C. 5 : 3
• D. 3:2

Answer 1

The Correct Option is D

Trains A and B were traveling in opposing directions at a 5:3 speed differential. 
Train A travels at a five-fold pace and Train B is traveling at a threefold pace. 

Suppose that train A's and train B's lengths are La and Lb. 
Forty-six seconds after the trains' front ends had crossed, the front end of A crossed the back end of B. 
Hence, Lb is the distance covered. It takes 46 seconds to complete this. 
It required an additional 69 seconds for the back ends of the trains to pass one another. 
The distance traveled is thus La. It takes 69 seconds to complete this.
\(\frac{\frac{la}{5x+3x}}{\frac{lb}{5x+3x}}=\frac{69}{46}\)
As they are traveling in opposing directions from one another, their relative speeds are 5x + 3x.
\(\frac{L_a}{L_b}=\frac{69}{46}\)
\(⇒\frac{3}{2}=3:2\)