Two linked ratios with a fixed total: ₹ 750 is distributed among A, B, and C such that A : B = 5 : 2 and B : C = 7 : 13. Determine A’s share in rupees.

Introduction / Context:
When two pairwise ratios are given with a common person in both, you can build a three-term ratio by aligning the shared term. After obtaining A : B : C, distribute the known total accordingly to find an individual’s share.

Given Data / Assumptions:

• A : B = 5 : 2.
• B : C = 7 : 13.
• Total amount = ₹ 750.

Concept / Approach:
Let A : B = 5x : 2x and B : C = 7y : 13y. Equalize B (2x = 7y) to combine ratios. Then compute A : B : C, sum the parts, find one-part value, and scale for A’s rupees.

Step-by-Step Solution:

Verification / Alternative check:
B’s share = 14 * 10 = ₹ 140; C’s = 26 * 10 = ₹ 260; sums to ₹ 750 and matches the given linked ratios.

Why Other Options Are Wrong:
₹ 140 is B’s share; ₹ 250 and ₹ 260 belong to neither A nor the computed parts for A; ₹ 300 does not fit the derived three-term split.

Common Pitfalls:
Adding ratios directly without aligning the common term B; forgetting to divide the total by the sum of all parts before scaling.

Final Answer:
₹ 350