Interpret decimal proportion precisely: 0.6 of a first number equals 0.09 of a second number. Find the ratio of the first number to the second number (first : second).

Introduction / Context:
Converting verbal proportional statements with decimals into a clean ratio is a core aptitude skill. The key is to isolate the ratio x : y from an equation of the form ax = by, then reduce to the smallest integer terms.

Given Data / Assumptions:

• 0.6 * (first number) = 0.09 * (second number).
• Both numbers are positive.

Concept / Approach:
If 0.6x = 0.09y, then x / y = 0.09 / 0.6. Simplify the fraction carefully by eliminating decimals (e.g., multiply numerator and denominator by 100) and then reduce by common factors to a clean ratio.

Step-by-Step Solution:

Verification / Alternative check:
Choose y = 20 and x = 3. Then 0.6x = 1.8 and 0.09y = 1.8, satisfying the condition.

Why Other Options Are Wrong:
2 : 3, 1 : 15, 20 : 3, and 5 : 18 do not satisfy 0.6x = 0.09y when tested; only 3 : 20 balances the equality.

Common Pitfalls:
Inverting the ratio (20 : 3) by mistake or dropping zeros incorrectly when clearing decimals. Always double-check by substituting simple values.

Final Answer:
3 : 20