MAT Exam 2021 Paper

Concept:When two trains cross each other, the distance covered is their combined length, and the rate of covering it is their relative speed.Explanation:Let the speed of the faster train be $x$ m/s and the speed of the slower train be $y$ m/s.In the same direction, relative speed is $(x-y)$ m/s.The faster train takes 60 seconds to pass completely, so$$\frac{240}{x-y}=60$$$$x-y=4$$In opposite directions, relative speed is $(x+y)$ m/s.They cross each other in 3 seconds, so$$\frac{240}{x+y}=3$$$$x+y=80$$Adding the two equations:$$(x-y)+(x+y)=4+80$$$$2x=84$$$$x=42\ \text{m/s}$$Answer:The speed of the faster train is $42$ m/s, i.e., Option A.