A is 40% less than B, and C is 40% of the sum of A and B. The difference between A and B is what percentage of C?

Options

A. 0.605
B. 0.64
C. 0.625
D. 0.6

Answer

To solve the problem step by step, let's define the variables and calculate accordingly.

### Step 1: Define B
Let's assume \( B = 100 \) (for simplicity, we can use any value, but 100 makes percentage calculations easier).

### Step 2: Calculate A
Since A is 40% less than B, we can calculate A as follows:
\[ A = B - 0.4B = 100 - 40 = 60 \]

### Step 3: Calculate the sum of A and B
Now we need to find the sum of A and B:
\[ A + B = 60 + 100 = 160 \]

### Step 4: Calculate C
C is defined as 40% of the sum of A and B:
\[ C = 0.4 \times (A + B) = 0.4 \times 160 = 64 \]

### Step 5: Calculate the difference between A and B
Now, we find the difference between A and B:
\[ \text{Difference} = B - A = 100 - 60 = 40 \]

### Step 6: Calculate the percentage of the difference with respect to C
To find what percentage the difference (40) is of C (64), we use the formula:
\[ \text{Percentage} = \left( \frac{\text{Difference}}{C} \right) \times 100 = \left( \frac{40}{64} \right) \times 100 \]
Calculating this gives:
\[ \text{Percentage} = \left( \frac{40}{64} \right) \times 100 = 62.5\% \]

### Final Answer
The difference between A and B is 62.5% of C.

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