MAT Exam 2022 Paper

Concept:Time is found by dividing distance by speed. The slower cyclist takes half an hour extra to reach the destination.Explanation:Let the required distance be $D$ km.Speed of slower cyclist $= 4$ kmph, speed of faster cyclist $= 5$ kmph.Time taken by slower cyclist $= \frac{D}{4}$ hours.Time taken by faster cyclist $= \frac{D}{5}$ hours.Since the slower cyclist arrives $0.5$ hours later, we write:$$\frac{D}{4} = \frac{D}{5} + \frac{1}{2}$$Subtract $\frac{D}{5}$ from both sides:$$\frac{D}{4} - \frac{D}{5} = \frac{1}{2}$$$$\frac{5D - 4D}{20} = \frac{1}{2}$$$$\frac{D}{20} = \frac{1}{2}$$$$D = 10 \text{ km}$$Convert to meters:$$D = 10 \times 1000 = 10000 \text{ m}$$Answer:The required distance is $10$ km or $10000$ m.Hence, the correct option is C.