The sum of two number is 37 and the difference of their squares is 185. Then the difference between the two numbers is :

Options

A. 10
B. 4
C. 5
D. 3

Answer

To solve the problem step by step, we will use the given information about the sum and the difference of the squares of two numbers.

### Step 1: Define the variables
Let the two numbers be \( x \) and \( y \).

### Step 2: Set up the equations
From the problem, we know:
1. The sum of the two numbers:
\[ x + y = 37 \quad (1) \]
2. The difference of their squares:
\[ x^2 - y^2 = 185 \quad (2) \]

### Step 3: Use the difference of squares formula
We can use the difference of squares formula, which states:
\[ x^2 - y^2 = (x + y)(x - y) \]
Substituting equation (1) into this formula, we get:
\[ (x + y)(x - y) = 185 \]
This can be rewritten as:
\[ 37(x - y) = 185 \]

### Step 4: Solve for \( x - y \)
Now, we can solve for \( x - y \):
\[ x - y = \frac{185}{37} \]
Calculating the right side:
\[ x - y = 5 \]

### Step 5: Conclusion
The difference between the two numbers \( x \) and \( y \) is:
\[ \boxed{5} \]