Shares from conditions on combined amounts: ₹ 5625 is divided among A, B, and C so that A receives 1/2 as much as B and C together receive, and B receives 1/4 of what A and C together receive. By how much does A’s share exceed B’s?

Introduction / Context:
Here, shares are tied to sums of the other shares. Forming equations from the narrative constraints and combining them with the total allows you to solve for each person’s amount precisely.

Given Data / Assumptions:

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

Concept / Approach:
Use the two linear relations to express A and C in terms of B (or vice versa), then use A + B + C = 5625 to find numerical values. Finally compute A − B.

Step-by-Step Solution:
From 2A = B + C and 4B = A + C ⇒ eliminate C.From 2A = B + C ⇒ C = 2A − B.Sub into 4B = A + C ⇒ 4B = A + (2A − B) = 3A − B ⇒ 5B = 3A ⇒ A = (5/3)B.Then C = 2A − B = 2*(5/3 B) − B = 7/3 B.Total = A + B + C = (5/3 + 1 + 7/3)B = 5B ⇒ 5B = 5625 ⇒ B = 1125, A = 1875.Difference A − B = 1875 − 1125 = 750.

Verification / Alternative check:
Check conditions: B + C = 1125 + 2625 = 3750 ⇒ A = 1875 = 1/2 of 3750; A + C = 1875 + 2625 = 4500 ⇒ B = 1125 = 1/4 of 4500.

Why Other Options Are Wrong:

• Other amounts do not satisfy both constraints simultaneously.

Common Pitfalls:

• Losing track of variables when substituting for C.

Final Answer:
Rs. 750