The difference of positive numbers is 1020. If 7.6% of the greater number is 12.4% of the smaller number, then the sum of two numbers is equal to.

Options

A. 3250
B. 4520
C. 3520
D. 4250

Answer

Let's solve the problem step by step.

### Step 1: Define the Variables
Let the greater number be \( x \) and the smaller number be \( y \). According to the problem, we know that:
\[ x - y = 1020 \quad \text{(1)} \]

### Step 2: Set Up the Percentage Equation
The problem states that 7.6% of the greater number is equal to 12.4% of the smaller number. This can be expressed as:
\[ 0.076x = 0.124y \quad \text{(2)} \]

### Step 3: Rearranging Equation (2)
From equation (2), we can express \( x \) in terms of \( y \):
\[ x = \frac{0.124}{0.076}y \]
Calculating the fraction:
\[ \frac{0.124}{0.076} = \frac{124}{76} = \frac{31}{19} \]
Thus, we have:
\[ x = \frac{31}{19}y \quad \text{(3)} \]

### Step 4: Substitute Equation (3) into Equation (1)
Now, we substitute equation (3) into equation (1):
\[ \frac{31}{19}y - y = 1020 \]
To combine the terms, we rewrite \( y \) as \( \frac{19}{19}y \):
\[ \frac{31}{19}y - \frac{19}{19}y = 1020 \]
This simplifies to:
\[ \frac{31 - 19}{19}y = 1020 \]
\[ \frac{12}{19}y = 1020 \]

### Step 5: Solve for \( y \)
Multiplying both sides by \( \frac{19}{12} \):
\[ y = 1020 \times \frac{19}{12} \]
Calculating this gives:
\[ y = 1020 \times 1.5833 = 1615 \]

### Step 6: Solve for \( x \)
Now, substitute \( y \) back into equation (3) to find \( x \):
\[ x = \frac{31}{19} \times 1615 \]
Calculating this gives:
\[ x = 31 \times 85 = 2635 \]

### Step 7: Find the Sum of \( x \) and \( y \)
Now, we can find the sum of the two numbers:
\[ x + y = 2635 + 1615 = 4250 \]

### Final Answer
Thus, the sum of the two numbers is:
\[ \boxed{4250} \]