Linear offsets in a three-way split: ₹ 710 is divided among A, B, and C such that A has ₹ 40 more than B and C has ₹ 30 more than A. Determine C’s share exactly.

Introduction / Context: When amounts differ by fixed increments, assign a base variable and build the others from it. Sum to the total to find the base, then recover each share directly. This linear approach is quick and robust.

Given Data / Assumptions:

• A = B + 40.
• C = A + 30 = B + 70.
• A + B + C = 710.

Concept / Approach: Let B = x. Then A = x + 40 and C = x + 70. Sum and solve for x. Then compute C.

Step-by-Step Solution:

Verification / Alternative check: A = 240, B = 200, C = 270. Differences: A − B = 40 and C − A = 30; sum 240 + 200 + 270 = 710.

Why Other Options Are Wrong: ₹ 300, ₹ 135, ₹ 235, ₹ 250 do not fit the linear offsets with the total 710 when computed.

Common Pitfalls: Misreading “more than” or forgetting to add both offsets when expressing C in terms of B.

Final Answer: ₹ 270