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 find the sum of the reciprocals of two numbers whose sum and product are given, we can follow these steps:

### Step 1: Define the Variables
Let the two numbers be \( a \) and \( b \).

### Step 2: Write Down the Given Information
From the problem, we know:
- The sum of the numbers:
\[ a + b = 11 \]
- The product of the numbers:
\[ a \cdot b = 18 \]

### Step 3: Find the Sum of the Reciprocals
The sum of the reciprocals of \( a \) and \( b \) can be expressed as:
\[ \frac{1}{a} + \frac{1}{b} = \frac{b + a}{ab} \]
Using the values we have:
\[ \frac{1}{a} + \frac{1}{b} = \frac{a + b}{a \cdot b} \]

### Step 4: Substitute the Known Values
Substituting the known values into the equation:
\[ \frac{1}{a} + \frac{1}{b} = \frac{11}{18} \]

### Step 5: Conclusion
Thus, the sum of the reciprocals of the two numbers is:
\[ \frac{11}{18} \]