2% of a = b, then b% of 10 is the same as

Options

A. 200% of a
B. 20% of a/100
C. 20% of a/10
D. 200% of a/10

Answer

To solve the problem step by step, we start with the given information and work towards expressing everything in terms of \( A \).

### Step 1: Understand the relationship between \( A \) and \( B \)
We are given that:
\[ 2\% \text{ of } A = B \]
This can be expressed mathematically as:
\[ B = \frac{2}{100} \times A = \frac{A}{50} \]

**Hint:** Remember that "percent" means "per hundred," so to convert a percentage to a decimal, divide by 100.

### Step 2: Calculate \( B\% \) of 10
Next, we need to find \( B\% \) of 10. This can be calculated as:
\[ B\% \text{ of } 10 = \frac{B}{100} \times 10 \]

**Hint:** When calculating a percentage of a number, multiply the percentage (as a fraction) by the number.

### Step 3: Substitute \( B \) into the equation
Now, substitute \( B = \frac{A}{50} \) into the equation from Step 2:
\[ B\% \text{ of } 10 = \frac{\frac{A}{50}}{100} \times 10 \]

**Hint:** When substituting values into an equation, ensure you maintain the correct order of operations.

### Step 4: Simplify the expression
Now simplify the expression:
\[ = \frac{A}{50 \times 100} \times 10 = \frac{A \times 10}{5000} = \frac{A}{500} \]

**Hint:** When simplifying fractions, look for common factors in the numerator and denominator.

### Final Answer
Thus, \( B\% \) of 10 is:
\[ \frac{A}{500} \]

### Summary
To summarize, we found that:
\[ B\% \text{ of } 10 = \frac{A}{500} \]