80% of a smaller number is 4 less than 40% of a larger number. The larger number is 85 greater than the smaller one. The sum of these two number is :

Options

A. 325
B. 425
C. 235
D. 500

Answer

To solve the problem step by step, we will define the smaller number as \( x \) and the larger number as \( y \).

### Step 1: Set up the equations based on the problem statement.
1. According to the problem, **80% of a smaller number is 4 less than 40% of a larger number**. This can be expressed as:
\[ 0.8x = 0.4y - 4 \]
Rearranging gives us:
\[ 0.4y - 0.8x = 4 \quad \text{(Equation 1)} \]

2. The problem also states that **the larger number is 85 greater than the smaller number**. This can be expressed as:
\[ y = x + 85 \quad \text{(Equation 2)} \]

### Step 2: Substitute Equation 2 into Equation 1.
Now we will substitute the value of \( y \) from Equation 2 into Equation 1:
\[ 0.4(x + 85) - 0.8x = 4 \]

### Step 3: Simplify the equation.
Distributing \( 0.4 \):
\[ 0.4x + 34 - 0.8x = 4 \]
Combining like terms:
\[ -0.4x + 34 = 4 \]

### Step 4: Isolate \( x \).
Subtract 34 from both sides:
\[ -0.4x = 4 - 34 \]
\[ -0.4x = -30 \]
Now, divide both sides by -0.4:
\[ x = \frac{-30}{-0.4} = 75 \]

### Step 5: Find \( y \) using the value of \( x \).
Now that we have \( x \), we can find \( y \) using Equation 2:
\[ y = x + 85 = 75 + 85 = 160 \]

### Step 6: Calculate the sum of \( x \) and \( y \).
Finally, we need to find the sum of the smaller and larger numbers:
\[ x + y = 75 + 160 = 235 \]

### Conclusion:
The sum of the two numbers is \( \boxed{235} \).

---