If 20% of A = 50% of B. then what per cent of A is B?

Options

A. 30%
B. 40%
C. 25%
D. 15%

Answer

To solve the problem step by step, we need to find out what percent of A is B given that 20% of A equals 50% of B.

### Step 1: Set up the equation
We start with the information given in the problem:
\[ 20\% \text{ of } A = 50\% \text{ of } B \]

This can be expressed mathematically as:
\[ \frac{20}{100} \times A = \frac{50}{100} \times B \]

### Step 2: Simplify the equation
We can simplify the percentages:
\[ \frac{1}{5} \times A = \frac{1}{2} \times B \]

### Step 3: Rearrange the equation
To find the relationship between A and B, we can rearrange the equation:
\[ A = \frac{1}{2} \times B \times 5 \]
\[ A = \frac{5}{2} \times B \]

### Step 4: Express B in terms of A
Now, we can express B in terms of A:
\[ B = \frac{2}{5} \times A \]

### Step 5: Find the percentage of A that is B
To find what percent of A is B, we can set up the following equation:
\[ \text{Percentage of A that is B} = \left( \frac{B}{A} \right) \times 100 \]

Substituting the expression for B:
\[ \text{Percentage of A that is B} = \left( \frac{\frac{2}{5} \times A}{A} \right) \times 100 \]

### Step 6: Simplify the percentage calculation
The A in the numerator and denominator cancels out:
\[ \text{Percentage of A that is B} = \left( \frac{2}{5} \right) \times 100 \]

### Step 7: Calculate the final percentage
Now, we calculate:
\[ \text{Percentage of A that is B} = 40\% \]

Thus, B is 40% of A.

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