MAT Exam 2024 Paper

Concept:When two runners reach the same time, their time taken must be equal.Explanation:Let the speed of Q be $x$ m/s.Since P runs $2 \frac{2}{3} = \frac{8}{3}$ times as fast as Q,Speed of P $= \frac{8}{3}x$.Let the winning post be at distance $d$ m from P’s starting point.Q gets a start of 80 m, so Q runs only $d - 80$ m.Time taken by P:$t_P = \dfrac{d}{\frac{8}{3}x} = \dfrac{3d}{8x}$Time taken by Q:$t_Q = \dfrac{d - 80}{x}$Since they reach the winning post at the same time:$\dfrac{3d}{8x} = \dfrac{d - 80}{x}$Cancel $x$ from both sides:$\dfrac{3d}{8} = d - 80$Multiply by 8:$3d = 8d - 640$$5d = 640$$d = 128$ mAnswer:$128$ mCorrect option: D. $128$ m