If 15% of Y is same as 21% of Z, then 12.5% of Y is equal to what per cent of Z?

Options

A. a. 20%
B. b. 17.5%
C. c. 13%
D. d. 9.5%

Answer

To solve the problem step by step, we start with the information given in the question.

### Step 1: Set up the equation
We know from the problem that:
\[ 15\% \text{ of } Y = 21\% \text{ of } Z \]
This can be written mathematically as:
\[ 0.15Y = 0.21Z \]

### Step 2: Express Y in terms of Z
To find Y in terms of Z, we can rearrange the equation:
\[ Y = \frac{0.21Z}{0.15} \]

### Step 3: Simplify the fraction
Now, we simplify the fraction:
\[ Y = \frac{21Z}{15} \]
\[ Y = \frac{21}{15}Z = \frac{7}{5}Z \]

### Step 4: Find 12.5% of Y
Next, we need to find 12.5% of Y:
\[ 12.5\% \text{ of } Y = 0.125Y \]
Substituting the expression we found for Y:
\[ 0.125Y = 0.125 \left(\frac{7}{5}Z\right) \]

### Step 5: Calculate the value
Now, we calculate:
\[ 0.125 \times \frac{7}{5}Z = \frac{7 \times 0.125}{5}Z \]
\[ = \frac{0.875}{5}Z \]
\[ = 0.175Z \]

### Step 6: Convert to percentage
To find out what percentage of Z this is, we convert 0.175Z to a percentage:
\[ 0.175Z = 17.5\% \text{ of } Z \]

### Conclusion
Thus, 12.5% of Y is equal to **17.5% of Z**.

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