5% of a=b, then b% of 20 is the same as ___________

Options

A. 20% of `(a)/(2)`
B. 50% of `(a)/(2)`
C. 50% of `(a)/(2)`
D. 20% of `(a)/(2)`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given equation
We start with the equation:
\[ 5\% \text{ of } A = B \]

### Step 2: Convert percentage to a fraction
We know that:
\[ 5\% = \frac{5}{100} \]
Thus, we can rewrite the equation as:
\[ \frac{5}{100} \times A = B \]

### Step 3: Simplify the equation
We can simplify \(\frac{5}{100}\) to \(\frac{1}{20}\):
\[ \frac{1}{20} \times A = B \]
This means:
\[ B = \frac{A}{20} \]

### Step 4: Find B percent of 20
Next, we need to find \(B\%\) of 20. We can express \(B\%\) as:
\[ B\% = \frac{B}{100} \]
So, \(B\%\) of 20 is:
\[ \frac{B}{100} \times 20 \]

### Step 5: Substitute the value of B
Now, we substitute \(B\) with \(\frac{A}{20}\):
\[ \frac{\frac{A}{20}}{100} \times 20 \]

### Step 6: Simplify the expression
This simplifies to:
\[ \frac{A}{20} \times \frac{20}{100} \]
The 20s cancel out:
\[ \frac{A}{100} \]

### Step 7: Conclusion
Thus, we find that:
\[ B\% \text{ of } 20 = \frac{A}{100} \]
This means that \(B\% \text{ of } 20\) is the same as \(A\%\).

### Final Answer:
B percent of 20 is the same as A percent.

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