There are five friends I, J, K, L and M. The income of K is more than the income of L but less than the income of M. The income of J is the least among all. The income of I is less than the income of K. Based on this information, whose income is the maximum among the five friends?

Introduction / Context:
This is a typical comparison question based on the incomes of five friends. Rather than giving actual income figures, the problem describes who earns more or less compared to others. You must use these comparative statements to identify the friend who has the highest income. Questions like this test basic logical ordering skills without needing any numerical calculations.

Given Data / Assumptions:
- Friends: I, J, K, L and M. - Income of K is more than income of L. - Income of K is less than income of M, so M earns more than K. - Income of J is the least among all five friends. - Income of I is less than income of K. - All incomes are distinct and comparable.

Concept / Approach:
The goal is to translate the verbal relationships into an ordered list from highest to lowest income. We look for the person who does not have anyone above them in this ordering. K is known to be above L and I but below M. J is at the bottom because J has the least income. Without knowing the exact positions of L and I relative to each other, we can still see that M is above K, and therefore above everyone else who is below K. That observation is enough to identify the maximum income holder.

Step-by-Step Solution:
Step 1: From K is more than L and I is less than K, both L and I lie below K in the income order. Step 2: From J is the least, we know J is at the very bottom, below everyone including L and I. Step 3: From K is less than M, we know M lies above K in the income order. Step 4: Combining these relations, we obtain a partial ordering: M above K, and K above I and L, and all four above J. Step 5: Even if we do not know whether I is above L or L is above I, both of them are below K, and K is below M. Therefore, no one can be above M in the income order. Step 6: Hence, M has the highest income among the five friends.

Verification / Alternative check:
To verify, you can assign sample incomes consistent with the conditions. For example, suppose M earns 50 units, K earns 40 units, I earns 30 units, L earns 25 units and J earns 10 units. All statements are satisfied: K (40) is more than L (25) but less than M (50), J (10) is the least, and I (30) earns less than K (40). In this sample, M is clearly the highest earner. No matter how you adjust the exact values while respecting the inequalities, M will always remain on top because the relation K less than M puts M above K, and K is already above I, L and far above J.

Why Other Options Are Wrong:
- L earns less than K, so L cannot have maximum income. - I earns less than K, so I cannot be at the top either. - K is explicitly stated to earn less than M, so K is not the maximum. - The information is sufficient and unambiguous, so the answer cannot be that it cannot be determined.

Common Pitfalls:
A common error is to focus on the lower end of the ranking and get confused about the relative positions of I and L, even though the question only asks for the maximum. Some students also misread K is less than M as the opposite, leading to incorrect placements. Carefully reading comparative phrases and maintaining a mental or written order diagram prevents these mistakes and makes the solution straightforward.

Final Answer:
The friend with the maximum income is M.