A bus is moving with a speed of 30 km/hr ahead of a car with a speed of 50 km/hr. How many kilometers apart are they if it takes 15 minutes for the car to catch up with the bus ?

Use relative speed and the distance = speed × time relation. Speed is distance per unit time [1]. Convert 15 minutes to hours: 15 min = 0.25 h [2]. The car’s speed relative to the bus equals 50 − 30 = 20 km/h (faster minus slower when moving in the same direction). Distance between them equals relative speed × time, so distance = 20 km/h × 0.25 h = 5 km. Hence the car will catch the bus after closing a 5 km gap, corresponding to option 1.

Sources

1. [1] Science-Class VII . NCERT(Revised ed 2025) > Chapter 8: Measurement of Time and Motion > 8.3 Speed > p. 113
2. [2] Science-Class VII . NCERT(Revised ed 2025) > Chapter 8: Measurement of Time and Motion > Speed = Total distance covered Total time taken > p. 114