Two relations on three shares: ₹ 5625 is divided among A, B, and C such that A receives half as much as B and C together, and B receives one-fourth as much as A and C together. Find (A + B).

Introduction / Context:
With two linear relations among three shares and a known total, set up simultaneous equations and solve. Express one or two shares in terms of a single variable to simplify the algebra and then compute the requested sum (A + B).

Given Data / Assumptions:

• A = (1/2)(B + C).
• B = (1/4)(A + C).
• A + B + C = 5625.

Concept / Approach:
From A = 0.5(B + C), write B in terms of A and C; combine with B = 0.25(A + C) to link A and C directly. Then find A, B, and hence A + B using the total.

Step-by-Step Solution:

Verification / Alternative check:
Check relations: A = 0.5(B + C) ⇒ 1875 = 0.5(1125 + 2625) = 0.5*3750 = 1875; B = 0.25(A + C) ⇒ 1125 = 0.25(1875 + 2625) = 0.25*4500 = 1125.

Why Other Options Are Wrong:
₹ 5000, ₹ 15000, ₹ 9000, ₹ 2500 contradict at least one relation or the total when computed.

Common Pitfalls:
Treating “half as much as” incorrectly or forgetting that both equations must hold simultaneously with the same A, B, C.

Final Answer:
₹ 3000