If 6 × (A’s capital) = 8 × (B’s capital) = 10 × (C’s capital), what is the ratio A : B : C of their capitals?

Introduction / Context:
When equal products are given, set each equal to a common constant and solve for the variables. This is a standard technique to extract ratios from equations like 6A = 8B = 10C.

Given Data / Assumptions:

• 6A = 8B = 10C = k (common constant).

Concept / Approach:
Express A, B, C in terms of k and compare. Because A = k/6, B = k/8, C = k/10, the ratio is the triplet of reciprocals 1/6 : 1/8 : 1/10. Clear denominators to reach integers.

Step-by-Step Solution:
A = k/6, B = k/8, C = k/10A : B : C = (1/6) : (1/8) : (1/10)Multiply by LCM(6,8,10) = 120 ⇒ 20 : 15 : 12

Verification / Alternative check:
Check: 6*20 = 120; 8*15 = 120; 10*12 = 120; all equal.

Why Other Options Are Wrong:
3 : 4 : 5 matches 6A = 8B = 10C only if scaled incorrectly; 6 : 8 : 10 is the product multipliers, not the capitals.

Common Pitfalls:
Confusing the coefficients (6, 8, 10) with the final ratio; remember the variables are inversely proportional to those coefficients.

Final Answer:
20 : 15 : 12