Mr. Karthik drives to his office at a constant average speed of 48 km/h. The time taken to cover the first 60% of the distance is 20 minutes more than the time taken to cover the remaining 40% of the distance. What is the total distance from his home to the office (in km)?

Introduction / Context:
This question tests understanding of average speed and the relationship between distance, speed, and time when different portions of a journey are considered. Although only one speed is mentioned, the question focuses on comparing the time taken for different fractions of the same total distance. This type of problem frequently appears in time and distance sections of aptitude tests.

Given Data / Assumptions:
- The overall average speed of Mr. Karthik is 48 km/h.
- The journey from home to office is a single trip with constant speed 48 km/h.
- The first 60% of the distance takes 20 minutes more than the last 40% of the distance.
- We assume straight travel at uniform speed with no breaks or delays.
- We need to find the entire distance between his home and office in kilometres.

Concept / Approach:
We use the basic formula distance = speed * time. If the speed is constant throughout the journey, then time is directly proportional to distance. That means the time taken to cover 60% of the distance and the time taken to cover 40% of the distance are proportional to 0.6 and 0.4 of the total distance, and their difference is given. By using the speed and the time difference, we can find the full distance.

Step-by-Step Solution:
Step 1: Let the total distance be D km.Step 2: Distance for the first part is 0.6D, and for the second part is 0.4D.Step 3: Since the speed is 48 km/h throughout, time for first 60% is t1 = 0.6D / 48 hours.Step 4: Time for last 40% is t2 = 0.4D / 48 hours.Step 5: The difference in time t1 - t2 equals 20 minutes, that is 1/3 hour.So, 0.6D / 48 - 0.4D / 48 = 1/3.Step 6: Simplify the left-hand side: (0.6D - 0.4D) / 48 = 0.2D / 48 = 1/3.Step 7: Therefore, 0.2D = 48 * (1/3) = 16, so D = 16 / 0.2 = 80 km.

Verification / Alternative check:
If the total distance is 80 km, then 60% of it is 48 km and 40% is 32 km. Time for the first 48 km at 48 km/h is 48 / 48 = 1 hour. Time for the last 32 km is 32 / 48 = 2/3 hour, which is 40 minutes. The difference between 1 hour and 40 minutes is 20 minutes, which matches the given condition, confirming that 80 km is correct.

Why Other Options Are Wrong:
- 40 km would make the time difference between the two parts smaller than 20 minutes.
- 50 km and 70 km similarly do not satisfy the condition when you compute the times for 60% and 40% segments at 48 km/h.
Only 80 km gives a time difference of exactly 20 minutes between the two parts of the journey.

Common Pitfalls:
One common error is to think that “average speed” means two different speeds were used, which can overcomplicate the problem. Here the average speed is the constant speed. Another pitfall is to convert 20 minutes incorrectly or to forget that 60% and 40% refer to fractions of the same total distance. Always work in consistent units and carefully translate percentage information into fractional distances.

Final Answer:
The distance from Karthik's home to his office is 80 km.