Who has the least money? – Four persons A, B, C, D with conditions: (i) A + B = C + D; (ii) B + D > A + C; (iii) A > B.

Introduction / Context:
We use sum equalities/inequalities to compare individuals. With A+B = C+D and B+D > A+C, we can deduce pairwise relations and identify the least amount.

Given Data / Assumptions:

• a + b = c + d.
• b + d > a + c.
• a > b.

Concept / Approach:
From the equality, express c in terms of a, b, d, then apply the inequality to compare d and a; finally, use c = a + b − d to rank c against b.

Step-by-Step Solution:
From a + b = c + d ⇒ c = a + b − d.From b + d > a + c and substituting c, we get b + d > a + (a + b − d) = 2a + b − d ⇒ 2d > 2a ⇒ d > a.Since a > b (given) and d > a, we compare c to b: c = a + b − d < a + b − a = b.Therefore, c is the least.

Verification / Alternative check:
Choose numbers satisfying d > a > b and set c = a + b − d; c will fall below b while equality (i) and inequality (ii) hold.

Why Other Options Are Wrong:
A and D are both greater than C by the deductions; B is greater than C because c < b.

Common Pitfalls:
Attempting to add/subtract the two original statements directly without substitution; missing the consequence d > a.

Final Answer:
C