Simple Interest — Relation among three principals: If A is the simple interest on B and B is the simple interest on C at the same rate and time, what is the relation among A, B, and C?

Introduction / Context:
Symbolic SI relationships test algebraic manipulation. If two statements about simple interest share the same rate and time, we can express each principal in terms of the others and eliminate the common factors.

Given Data / Assumptions:

• A is SI on principal B at rate r and time t ⇒ A = B * r * t
• B is SI on principal C at the same rate r and time t ⇒ B = C * r * t

Concept / Approach:
From B = C r t, substitute into A = B r t to get A = (C r t) r t = C (r t)^2. Use these to connect A, B, C by eliminating r t.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• A2 = B C or C2 = A B do not match the algebra.
• A B C = 1 and A = B = C are unrelated to SI scaling.

Common Pitfalls:

• Treating r as percent value instead of decimal in algebra; only the product r t matters.

Final Answer:
B^2 = A C.