If 30% of A is added to 40% of B, the answer is 80% of B. What percentage of A is B?

Options

A. 0.3
B. 0.4
C. 0.7
D. 0.75

Answer

To solve the problem step by step, we need to set up the equation based on the information given in the question.

### Step 1: Set up the equation
We know from the problem statement that:
\[ 30\% \text{ of } A + 40\% \text{ of } B = 80\% \text{ of } B \]

### Step 2: Convert percentages to decimals
To eliminate the percentages, we can express them in decimal form:
\[ 0.3A + 0.4B = 0.8B \]

### Step 3: Rearrange the equation
Next, we can rearrange the equation to isolate terms involving \(B\):
\[ 0.3A + 0.4B - 0.8B = 0 \]
This simplifies to:
\[ 0.3A - 0.4B = 0 \]

### Step 4: Solve for A in terms of B
Now, we can express \(A\) in terms of \(B\):
\[ 0.3A = 0.4B \]
Dividing both sides by \(0.3\):
\[ A = \frac{0.4B}{0.3} \]
This simplifies to:
\[ A = \frac{4}{3}B \]

### Step 5: Find the percentage of A that is B
To find what percentage of \(A\) is \(B\), we can express \(B\) in terms of \(A\):
\[ B = \frac{3}{4}A \]
Now, we can express this as a percentage:
\[ \text{Percentage of } A \text{ that is } B = \left( \frac{B}{A} \right) \times 100 \]
Substituting \(B = \frac{3}{4}A\):
\[ \text{Percentage of } A \text{ that is } B = \left( \frac{\frac{3}{4}A}{A} \right) \times 100 \]
This simplifies to:
\[ \text{Percentage of } A \text{ that is } B = \frac{3}{4} \times 100 = 75\% \]

### Final Answer
Thus, the percentage of \(A\) that is \(B\) is **75%**.

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