In each of these questions, relationships between elements are shown. Based on the statements A > B < P and Q < R > P, determine which of the conclusions B < R and Q > A logically follow from the given information.

Introduction / Context:
This logical reasoning problem again involves chained inequalities among several variables. The goal is to determine which of two proposed conclusions must hold for every possible assignment of numbers that satisfies the given statements. These questions are common in competitive exams and test the ability to work with relative, not absolute, values.

Given Data / Assumptions:

• A > B.
• B < P.
• Q < R.
• R > P.
• Conclusion I: B < R.
• Conclusion II: Q > A.

Concept / Approach:
We visualise the variables on a number line. From the given inequalities, we find a chain for some of them. When a variable is greater than one and another is greater than it, we can join those facts to compare variables that do not directly appear together. At the same time, if there is no way to connect two variables with a consistent chain, then no certain comparison can be made between them.

Step-by-Step Solution:
Step 1: Use the relations involving B, P and R. We are told B < P and R > P. That gives B < P < R. From this chain we can conclude B < R. Hence conclusion I is always true. Step 2: Now analyse conclusion II, Q > A. The statements tell us that Q < R and A > B. Apart from that, Q and A are in different parts of the inequality structure, with no relation linking them directly or through an unbroken chain. This means two types of numeric assignments are possible without breaking any given condition: one where Q is greater than A and another where Q is less than or equal to A. Since both Q > A and Q ≤ A can be made consistent with all original statements, there is no single relation between Q and A that must always hold. Thus conclusion II is not guaranteed to be true.

Verification / Alternative check:
Take one numeric example: let B = 1, P = 3, R = 5, and choose A = 4 (which is greater than B) and Q = 2 (which is less than R). All original inequalities are satisfied: A > B (4 > 1), B < P (1 < 3), Q < R (2 < 5), and R > P (5 > 3). In this setup Q = 2 is less than A = 4, so Q > A is false. This shows conclusion II does not always hold. On the other hand, B < R becomes 1 < 5, which is correct. You can try other numbers and you will always find B < R is satisfied and conclusion I holds.

Why Other Options Are Wrong:

• Option b (only conclusion II) is wrong because conclusion II can fail.
• Option c (either I or II) is not right since we always have I true and II can be false.
• Option d (neither) ignores that B < R is definitely true.
• Option e (both) is wrong because we have demonstrated that II does not follow.

Common Pitfalls:
One common error is to assume that all variables are comparable simply because they appear in the same problem. Without a direct or indirect chain of inequalities, you cannot fix the relative order of two variables. Learners may also confuse Q < R and A > B and imagine some link between them that does not actually exist. Always stick strictly to what is given.

Final Answer:
Only conclusion I follows, so option a is correct.