The sum and product of two numbers are 11 and 18 respectively. The sum of their reciprocals is

Options

A. `(2)/(11)`
B. `(11)/(2)`
C. `(18)/(11)`
D. `(11)/(18)`

Answer

To solve the problem step by step, we need to find the sum of the reciprocals of two numbers given their sum and product.

### Step 1: Define the variables
Let the two numbers be \( x \) and \( y \). According to the problem, we have:
- The sum of the numbers: \( x + y = 11 \)
- The product of the numbers: \( x \cdot y = 18 \)

### Step 2: Write the formula for the sum of reciprocals
The sum of the reciprocals of \( x \) and \( y \) can be expressed as:
\[ \frac{1}{x} + \frac{1}{y} = \frac{y + x}{xy} \]

### Step 3: Substitute the known values into the formula
From Step 1, we know:
- \( x + y = 11 \)
- \( x \cdot y = 18 \)

Now, substituting these values into the formula:
\[ \frac{1}{x} + \frac{1}{y} = \frac{x + y}{xy} = \frac{11}{18} \]

### Step 4: Final answer
Thus, the sum of the reciprocals of the two numbers is:
\[ \frac{11}{18} \]