MAT Exam 2020 Paper

Concept:The swimmers move along perpendicular directions (South and East), so the distance between them after 2 hours forms the hypotenuse of a right triangle.Explanation:Let the speed of the faster swimmer be $x$ km/h.Speed of the slower swimmer is $75\%$ of $x$:$$= \frac{75}{100}x = \frac{3x}{4}\ \text{km/h}$$In 2 hours, distance covered by faster swimmer:$$2x\ \text{km}$$Distance covered by slower swimmer:$$\frac{3x}{4} \times 2 = \frac{3x}{2}\ \text{km}$$After 2 hours, distance between them is $100$ km.Using Pythagoras theorem:$$(2x)^2 + \left(\frac{3x}{2}\right)^2 = (100)^2$$$$4x^2 + \frac{9x^2}{4} = 10000$$$$\frac{16x^2 + 9x^2}{4} = 10000$$$$\frac{25x^2}{4} = 10000$$$$x^2 = 1600$$$$x = 40\ \text{km/h}$$Answer:Speed of the faster swimmer is $40$ km/h.Correct option: C. $40$ km/h.