If x is one-ninth of y, then find 'a' such that x :y =12 :a

Answer

To solve the problem step by step, we start with the information given:

1. **Understanding the relationship between x and y**:
- We know that \( x \) is one-ninth of \( y \). This can be expressed mathematically as:
\[ x = \frac{1}{9}y \]

2. **Setting up the ratio**:
- We need to find \( a \) such that the ratio \( x : y = 12 : a \). This can be written as:
\[ \frac{x}{y} = \frac{12}{a} \]

3. **Substituting the value of \( \frac{x}{y} \)**:
- From the first step, we have \( \frac{x}{y} = \frac{1}{9} \). We can substitute this into our ratio equation:
\[ \frac{1}{9} = \frac{12}{a} \]

4. **Cross-multiplying to solve for \( a \)**:
- To eliminate the fractions, we can cross-multiply:
\[ 1 \cdot a = 12 \cdot 9 \]
- This simplifies to:
\[ a = 108 \]

5. **Final answer**:
- Therefore, the value of \( a \) is:
\[ a = 108 \]