Proportional division with a combined constraint: ₹ 385 is divided among A, B, and C such that A receives 2/9 of what B and C receive together. Determine A’s share accurately.

Introduction / Context: This is a classic share-splitting question with a condition tying one person’s amount to the sum of the others. Reducing the condition to one unknown for the combined share makes the arithmetic straightforward.

Given Data / Assumptions:

• Total amount = ₹ 385.
• A = (2/9) * (B + C).

Concept / Approach: Let T = B + C. Then A = (2/9)T and total is A + T = 385. Solve for T and then find A directly from the relation.

Step-by-Step Solution:

Verification / Alternative check: Check: A + T = 70 + 315 = 385; condition holds because 2/9 of 315 is 70.

Why Other Options Are Wrong: ₹ 77, ₹ 82.50, and ₹ 85 do not satisfy A = (2/9)(385 − A); ₹ 90 is also inconsistent with the required fraction.

Common Pitfalls: Treating 2/9 as a part of the whole instead of specifically of (B + C); ensure you form A + (B + C) for the total.

Final Answer: Rs. 70