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 will start by translating the given information into a mathematical equation.

### Step 1: Set up the equation
We know from the problem statement that:
- 30% of A + 40% of B = 80% of B

This can be expressed mathematically as:
\[ 0.3A + 0.4B = 0.8B \]

### Step 2: Rearrange the equation
Next, we will rearrange the equation to isolate terms involving B on one side:
\[ 0.3A = 0.8B - 0.4B \]
\[ 0.3A = 0.4B \]

### Step 3: Simplify the equation
Now, we can simplify the equation:
\[ 0.3A = 0.4B \]

### Step 4: Express A in terms of B
To find the relationship between A and B, we can express A in terms of B:
\[ A = \frac{0.4B}{0.3} \]
\[ A = \frac{4}{3}B \]

### Step 5: Find the percentage of B in terms of A
Now, we need to find what percentage of A is B. We can express B in terms of A:
\[ B = \frac{3}{4}A \]

### Step 6: Calculate the percentage
To find the percentage of A that is B, we use the formula:
\[ \text{Percentage of A that is B} = \left( \frac{B}{A} \right) \times 100 \]
Substituting B from the previous step:
\[ \text{Percentage of A that is B} = \left( \frac{\frac{3}{4}A}{A} \right) \times 100 \]
\[ = \frac{3}{4} \times 100 = 75\% \]

### Conclusion
Thus, the percentage of A that is B is **75%**.