25% of what amount of money is equal to `12(1)/(2)`% of 180 ?

Options

A. ? 120
B. ? 75
C. ? 80
D. ? 90

Answer

To solve the problem step by step, we need to determine what amount of money (let's call it \( x \)) corresponds to 25% being equal to \( 12\frac{1}{2}\% \) of 180.

### Step-by-Step Solution:

1. **Convert the percentage to a fraction**:
- \( 12\frac{1}{2}\% \) can be converted to an improper fraction.
- \( 12\frac{1}{2} = 12 + \frac{1}{2} = \frac{25}{2} \).
- So, \( 12\frac{1}{2}\% = \frac{25}{2}\% \).

2. **Express the percentage as a decimal**:
- To convert \( \frac{25}{2}\% \) to a decimal, we divide by 100.
- \( \frac{25}{2} \div 100 = \frac{25}{200} = \frac{1}{8} \).

3. **Calculate \( 12\frac{1}{2}\% \) of 180**:
- Now we find \( \frac{1}{8} \) of 180.
- \( \frac{1}{8} \times 180 = \frac{180}{8} = 22.5 \).

4. **Set up the equation**:
- According to the problem, \( 25\% \) of \( x \) is equal to \( 22.5 \).
- We can express this as:
\[ 0.25x = 22.5 \]

5. **Solve for \( x \)**:
- To isolate \( x \), divide both sides of the equation by \( 0.25 \):
\[ x = \frac{22.5}{0.25} \]

6. **Calculate \( x \)**:
- \( \frac{22.5}{0.25} = 22.5 \times 4 = 90 \).

### Final Answer:
The required amount \( x \) is \( 90 \).

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