Laxmi walks northwards at 20 km/h and Prasanna walks southwards at 30 km/h, starting from the same point at the same time. How far apart (in km) will they be after 60 minutes?

Introduction / Context:
This problem is a straightforward application of relative speed when two people move in opposite directions. It checks if you correctly understand that when two objects move away from each other, the rate at which the distance between them increases is the sum of their individual speeds.

Given Data / Assumptions:

• Laxmi walks northwards at 20 km/h.
• Prasanna walks southwards at 30 km/h.
• They start from the same point at the same time.
• Time interval considered = 60 minutes = 1 hour.

Concept / Approach:
When two people move in exactly opposite directions from the same starting point, their separation grows at the sum of their speeds. Hence, the relative speed between them is 20 km/h + 30 km/h. Multiplying this relative speed by the time gives the distance between them after the given time.

Step-by-Step Solution:
Speed of Laxmi = 20 km/h. Speed of Prasanna = 30 km/h. Relative speed (moving in opposite directions) = 20 + 30 = 50 km/h. Time of travel = 60 minutes = 1 hour. Distance between them after 1 hour = relative speed * time. Distance = 50 * 1 = 50 km.

Verification / Alternative check:
You can also compute separate distances: in 1 hour, Laxmi walks 20 km north, and Prasanna walks 30 km south. The total separation is 20 km + 30 km = 50 km, matching the previous calculation.

Why Other Options Are Wrong:

• 24 km and 30 km ignore that both are moving and only consider one person's distance.
• 42 km is just a random value and does not correspond to the sum of the two distances after 1 hour.

Common Pitfalls:
A common mistake is to subtract the speeds instead of adding them when objects move in opposite directions. Another is to forget converting time correctly if it is not already in hours. Here, time is already 1 hour, so the calculation is simple.

Final Answer:
After 60 minutes, Laxmi and Prasanna are 50 km apart.