Decimal-to-ratio conversion: If 0.8 × A = 0.09 × B, determine the simplest ratio A : B.

Introduction / Context:
Converting linear equations with decimals to clean ratios is a staple aptitude skill. Here, we solve for A/B from the equation 0.8A = 0.09B and then write A : B in lowest integer terms.

Given Data / Assumptions:
0.8A = 0.09B; A and B are positive.

Concept / Approach:
Isolate A/B: A/B = 0.09 / 0.8. Then express as a fraction and reduce to the simplest whole-number ratio.

Step-by-Step Solution:
A/B = 0.09 / 0.8. Convert to fractions: 0.09 = 9/100, 0.8 = 8/10 = 4/5. A/B = (9/100) / (4/5) = (9/100) * (5/4) = 45/400 = 9/80. Hence, A : B = 9 : 80.

Verification / Alternative check:
Take A = 9 and B = 80. Then 0.8A = 7.2 and 0.09B = 7.2, satisfying the equation.

Why Other Options Are Wrong:
3 : 80, 7 : 80, 80 : 9, 9 : 8 are not equal to 9 : 80 and will not satisfy 0.8A = 0.09B.

Common Pitfalls:
Mishandling decimals or forgetting to invert the divisor when dividing fractions. Carefully convert decimals to fractions before simplifying.

Final Answer:
9 : 80