20% of a=b, then b% of 20 is the same as___________ of a

Options

A. 4%
B. 5%
C. 20%
D. 30%

Answer

To solve the problem step by step, we start with the given information and work through the calculations systematically.

### Step 1: Understand the given relationship
We know that:
\[ 20\% \text{ of } A = B \]
This can be expressed mathematically as:
\[ \frac{20}{100} \times A = B \]
or simplified to:
\[ B = \frac{1}{5} A \]

**Hint:** Understand that "20% of A" means you are taking 20 parts out of 100 parts of A.

### Step 2: Express B in terms of A
From the equation \( B = \frac{1}{5} A \), we can also express A in terms of B:
\[ A = 5B \]

**Hint:** Rearranging equations can help you express one variable in terms of another.

### Step 3: Set up the equation for B% of 20
Next, we need to find \( B\% \text{ of } 20 \):
\[ B\% \text{ of } 20 = \frac{B}{100} \times 20 \]

**Hint:** Remember that "X% of Y" can be calculated using the formula \( \frac{X}{100} \times Y \).

### Step 4: Substitute B with its expression in terms of A
Substituting \( B = \frac{1}{5} A \) into the equation:
\[ B\% \text{ of } 20 = \frac{\frac{1}{5} A}{100} \times 20 \]
This simplifies to:
\[ = \frac{A}{500} \times 20 \]
\[ = \frac{20A}{500} \]
\[ = \frac{A}{25} \]

**Hint:** When substituting, ensure you simplify the fractions correctly.

### Step 5: Find the equivalent percentage of A
Now, we need to express \( \frac{A}{25} \) in terms of a percentage of A:
\[ \frac{A}{25} = X\% \text{ of } A \]
This means:
\[ X\% = \frac{1}{25} \times 100 \]
\[ X = 4 \]

**Hint:** To find what percentage one number is of another, you can set up a ratio and convert it to a percentage.

### Conclusion
Therefore, \( B\% \text{ of } 20 \) is the same as \( 4\% \text{ of } A \).

**Final Answer:** B% of 20 is the same as 4% of A.