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

To find the distance between the car and the bus, we use the concept of relative speed. Since both vehicles are moving in the same direction, the relative speed is the difference between their speeds.

1. Calculate Relative Speed: Subtract the bus speed from the car speed. 50 km/hr minus 30 km/hr equals 20 km/hr. This is the speed at which the car closes the gap.

2. Convert Time: The time given is 15 minutes. To match the speed unit of hours, convert minutes to hours by dividing by 60. 15 divided by 60 equals 0.25 hours or 1/4 of an hour.

3. Calculate Distance: Distance is speed multiplied by time. Multiply the relative speed of 20 km/hr by the time of 0.25 hours. 20 times 0.25 equals 5 km.

Therefore, the car and bus were 5 km apart. Option A is the correct answer.