Difficulty: Medium
Correct Answer: ₹ 3000
Explanation:
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:
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:
A = (1/2)(B + C) ⇒ 2A = B + C ⇒ B = 2A − C.B = (1/4)(A + C) ⇒ 2A − C = (1/4)(A + C).Multiply by 4: 8A − 4C = A + C ⇒ 7A = 5C ⇒ C = (7/5)A.Then B = 2A − C = 2A − (7/5)A = (3/5)A.Total: A + B + C = A + (3/5)A + (7/5)A = 3A = 5625 ⇒ A = 1875; B = 1125.A + B = 1875 + 1125 = ₹ 3000.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
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