MAT Exam 2021 Paper

Concept:Speed is the ratio of distance covered to time taken.The runner with the higher speed runs faster.Explanation:Distance covered by $A$ in one round on the inner track:$$2\pi \times 100 = 200\pi \ \text{m}$$Distance covered by $B$ in one round on the outer track:$$2\pi \times 102 = 204\pi \ \text{m}$$Time taken by $A$:$$1 \text{ min } 30 \text{ s} = 90 \text{ s}$$Time taken by $B$:$$1 \text{ min } 32 \text{ s} = 92 \text{ s}$$Speed of $A$:$$\frac{200\pi}{90} = \frac{20\pi}{9}$$Speed of $B$:$$\frac{204\pi}{92} = \frac{51\pi}{23}$$Compare the speeds:$$\frac{20}{9} > \frac{51}{23}$$Therefore, speed of $A$ is greater than speed of $B$.Answer:$A$ runs faster.Correct option: A. $A$