Kishlay travels three equal distances at speeds of 10 km/h, 30 km/h and 2 km/h and takes a total time of 38 minutes. Find the total distance in kilometres.

Introduction / Context:
This question tests the standard time, speed and distance concept where a person covers equal distances at different speeds. Many aptitude tests include such problems because they check understanding of the relationship between speed, time and distance, and how to handle situations where segments of a journey are equal in length but covered at different speeds. Here we need to use the fact that total time is the sum of times for each segment, and all three segments have the same distance.

Given Data / Assumptions:
The journey has three equal parts in terms of distance. Speeds on these three parts are 10 km/h, 30 km/h and 2 km/h. Total time taken for the whole journey is 38 minutes. We assume uniform speed on each segment and no waiting time between segments.

Concept / Approach:
The basic relationship is distance = speed * time, or equivalently time = distance / speed. When equal distances are travelled at different speeds, it is convenient to let the common distance of each segment be d kilometres. Then we express the time for each segment in hours, sum them, and equate this total to the given overall time converted into hours. Finally, we solve for d and multiply by the number of segments to get the total distance travelled by Kishlay.

Step-by-Step Solution:
Step 1: Let the distance of each segment be d kilometres. Step 2: Time for first segment at 10 km/h is d / 10 hours. Step 3: Time for second segment at 30 km/h is d / 30 hours. Step 4: Time for third segment at 2 km/h is d / 2 hours. Step 5: Total time in hours is 38 minutes = 38 / 60 hours. Step 6: Form the equation d / 10 + d / 30 + d / 2 = 38 / 60. Step 7: Take common denominator 30 on the left side: (3d + d + 15d) / 30 = 19d / 30. Step 8: So 19d / 30 = 38 / 60. Simplify the right side: 38 / 60 = 19 / 30. Step 9: Therefore 19d / 30 = 19 / 30, which implies d = 1 kilometre. Step 10: There are three equal segments, so total distance = 3 * d = 3 km.

Verification / Alternative check:
If each segment is 1 km, then time at 10 km/h is 1 / 10 hour, at 30 km/h is 1 / 30 hour and at 2 km/h is 1 / 2 hour. Converting to minutes, these are 6 minutes, 2 minutes and 30 minutes respectively. The total time is 6 + 2 + 30 = 38 minutes, which matches the given total time. This confirms that the total distance of 3 kilometres is consistent with the information in the question and therefore correct.

Why Other Options Are Wrong:
2 km would give each segment as 2 / 3 km, and the total time would no longer add up to 38 minutes. 1 km would mean each segment is only 1 / 3 km, which clearly reduces total time too much. 4 km would make each segment longer than 1 km and would result in a total time greater than 38 minutes. Thus only 3 km satisfies the time condition exactly for the three speeds.

Common Pitfalls:
A common mistake is to take the simple average of the three speeds instead of correctly using the time formula for equal distances. Another frequent error is forgetting to convert minutes into hours before forming the equation, which leads to wrong proportions. Some learners also mistakenly assume equal times instead of equal distances. Carefully setting up the variable d for equal distances and correctly converting units avoids these errors in similar time, speed and distance questions.

Final Answer:
The total distance covered by Kishlay when he travels three equal distances at the given speeds in a total of 38 minutes is 3 km.