If `x%` of `a=y%` of b, then `z%` of b is

Options

A. `(abz)/(100)`
B. `(yxz)/(axx100)`
C. `(axz)/(yxx100)`
D. `(abz)/(yxx100)`

Answer

To solve the problem, we start with the given equation:

1. **Understanding the Equation**:
We know that \( x\% \) of \( a \) is equal to \( y\% \) of \( b \). This can be expressed mathematically as:
\[ \frac{x}{100} \cdot a = \frac{y}{100} \cdot b \]

2. **Rearranging the Equation**:
To find the relationship between \( a \) and \( b \), we can rearrange the equation:
\[ x \cdot a = y \cdot b \]
Dividing both sides by \( y \):
\[ b = \frac{x \cdot a}{y} \]

3. **Finding \( z\% \) of \( b \)**:
We need to find \( z\% \) of \( b \). This can be expressed as:
\[ z\% \text{ of } b = \frac{z}{100} \cdot b \]

4. **Substituting \( b \)**:
Now, we substitute the value of \( b \) from our earlier equation:
\[ z\% \text{ of } b = \frac{z}{100} \cdot \left(\frac{x \cdot a}{y}\right) \]

5. **Simplifying the Expression**:
Now we simplify the expression:
\[ z\% \text{ of } b = \frac{z \cdot x \cdot a}{100 \cdot y} \]

6. **Final Expression**:
Therefore, we can express \( z\% \) of \( b \) as:
\[ z\% \text{ of } b = \frac{a \cdot x \cdot z}{y \cdot 100} \]

Thus, the answer is:
\[ \frac{a \cdot x \cdot z}{y \cdot 100} \]