A’s capital equals twice B’s, and B’s capital equals three times C’s. What is the ratio of capitals A : B : C?

Introduction / Context:
Converting nested relations into a single three-term ratio is a standard step in partnership and ratio problems. We align all terms to a common base (here, C) to obtain A : B : C directly.

Given Data / Assumptions:

• A = 2B.
• B = 3C.

Concept / Approach:
Substitute B = 3C into A = 2B to express all three in terms of C, then read off the ratio.

Step-by-Step Solution:
B = 3C. A = 2B = 2 * 3C = 6C. Therefore, A : B : C = 6C : 3C : C = 6 : 3 : 1.

Verification / Alternative check:
The ratio satisfies the original statements: A = 2B (6 : 3) and B = 3C (3 : 1).

Why Other Options Are Wrong:
2 : 1 : 3 scrambles the order. 1 : 2 : 6 is inverted. 1 : 3 : 6 swaps positions and does not meet A = 2B.

Common Pitfalls:
Mixing the directions (e.g., thinking B = 2A) or failing to keep a consistent base when forming the combined ratio.

Final Answer:
6 : 3 : 1