Two bikers A and B start at the same time from two different points and ride towards each other along a straight road. Biker A rides at a constant speed of 75 km/h and biker B rides at a constant speed of 60 km/h. They meet exactly after 20 minutes. What was the distance (in kilometres) between them when they started?

Introduction / Context:
This question tests the concept of relative speed when two objects are moving towards each other. It is a standard type of time and distance problem that appears frequently in aptitude exams. The key skill is converting minutes to hours and correctly adding the individual speeds to obtain effective relative speed for objects moving in opposite directions.

Given Data / Assumptions:

Speed of biker A = 75 km/h.
Speed of biker B = 60 km/h.
They ride towards each other along a straight line.
They meet after 20 minutes from the time they start.
We assume their speeds remain constant during the entire journey.

Concept / Approach:
When two bodies move towards each other along a straight line, their relative speed is the sum of their individual speeds. Total distance between them is equal to relative speed multiplied by the time taken to meet. Since the speeds are given in km/h, the time must be converted into hours. The resulting product gives the initial separation distance between the two bikers.

Step-by-Step Solution:
Step 1: Convert the meeting time into hours: 20 minutes = 20 / 60 hours = 1 / 3 hour. Step 2: Compute the relative speed when they move towards each other: relative speed = 75 + 60 = 135 km/h. Step 3: Use the relation distance = speed * time. Here, distance between them initially = relative speed * time taken to meet. Step 4: Distance = 135 * (1 / 3) = 45 kilometres. Step 5: Therefore, the initial distance between biker A and biker B was 45 km.

Verification / Alternative check:
We can check by computing how far each biker travels in 1 / 3 hour. Biker A covers 75 * (1 / 3) = 25 km, and biker B covers 60 * (1 / 3) = 20 km. The sum 25 + 20 = 45 km matches the initial distance between them, confirming that our calculation is correct. The meeting point is somewhere between the two starting points such that these individual distances add up to the total separation.

Why Other Options Are Wrong:
If the distance were 60 km, at a combined speed of 135 km/h, they would need 60 / 135 hours, which is less than 20 minutes. A distance of 30 km or 15 km would mean even smaller meeting times than 20 minutes. A value of 40 km still does not match the given time when checked with the relative speed. Only 45 km gives exactly 20 minutes for them to meet.

Common Pitfalls:
Typical mistakes include subtracting speeds instead of adding them when the objects move towards each other, or forgetting to convert minutes into hours, which leads to large numerical errors. Some learners also apply distance = speed / time incorrectly instead of speed * time. Carefully identifying the direction of motion and ensuring consistent units avoids these errors.

Final Answer:
The bikers were initially separated by 45 kilometres.