Two persons K and L start walking towards each other at 4:00 p.m. from points 17.5 km apart. K walks at 3 km/h and L walks at 4 km/h. At what time will they meet?

Introduction / Context:
This question involves two people walking towards each other from two different points that are a known distance apart. It tests your understanding of relative speed when objects move towards each other, as well as your ability to convert time in hours to a clock format. Problems like this are very common in the time and distance section of aptitude exams.

Given Data / Assumptions:
- Distance between K and L at the start = 17.5 km.
- K walks at a constant speed of 3 km/h.
- L walks at a constant speed of 4 km/h.
- Both start walking towards each other at exactly 4:00 p.m.
- They continue to walk without stopping until they meet.

Concept / Approach:
When two people move towards each other along a straight line, their effective or relative speed is the sum of their individual speeds. The time needed to meet is then found by dividing the initial distance between them by this relative speed. Finally, we add this time interval to the starting time to get the exact meeting time on the clock.

Step-by-Step Solution:
Step 1: Calculate the relative speed.Relative speed = speed of K + speed of L = 3 km/h + 4 km/h = 7 km/h.Step 2: Use the formula time = distance / speed to find the time taken to meet.Time taken to meet = 17.5 km / 7 km/h = 2.5 hours.Step 3: Convert 2.5 hours to hours and minutes.2.5 hours = 2 hours 30 minutes.Step 4: Add this duration to the starting time of 4:00 p.m.4:00 p.m. + 2 hours 30 minutes = 6:30 p.m.

Verification / Alternative check:
In 2.5 hours, K will walk 3 * 2.5 = 7.5 km, and L will walk 4 * 2.5 = 10 km. The total distance covered by both together is 7.5 km + 10 km = 17.5 km, which is exactly the original separation between them. This confirms that they meet after 2.5 hours, that is, at 6:30 p.m.

Why Other Options Are Wrong:
- 6:00 p.m. would correspond to only 2 hours of walking, in which they would cover 3 * 2 + 4 * 2 = 14 km, less than 17.5 km.
- 5:45 p.m. corresponds to 1 hour 45 minutes, which is too early; they would not have covered the full 17.5 km together.
- 5:52 p.m. is an arbitrary time that does not match a precise division of the distance by their relative speed.
Thus, 6:30 p.m. is the only correct meeting time.

Common Pitfalls:
A common mistake is to subtract the speeds instead of adding them when objects move towards each other. Another error is to mis-handle the conversion of decimal hours to minutes, for example confusing 0.5 hours with 50 minutes instead of 30 minutes. Always convert decimal fractions of an hour using the fact that 1 hour = 60 minutes, so 0.5 hour = 30 minutes and 0.25 hour = 15 minutes.

Final Answer:
K and L will meet at 6:30 p.m.