The sum and product of two numbers are 12 and 35 respectively. What will be the sum of their reciprocals?

Options

A. `1/3`
B. `1/5`
C. `12/35`
D. `35/12`

Answer

To find the sum of the reciprocals of two numbers whose sum is 12 and product is 35, we can follow these steps:

### Step 1: Define the Variables
Let the two numbers be \( A \) and \( B \). According to the problem, we have:
- \( A + B = 12 \) (sum of the numbers)
- \( A \times B = 35 \) (product of the numbers)

### Step 2: Write the Expression for the Sum of Reciprocals
The sum of the reciprocals of \( A \) and \( B \) can be expressed as:
\[ \frac{1}{A} + \frac{1}{B} \]
This can be rewritten using a common denominator:
\[ \frac{1}{A} + \frac{1}{B} = \frac{B + A}{AB} \]

### Step 3: Substitute the Known Values
From Step 1, we know:
- \( A + B = 12 \)
- \( A \times B = 35 \)

Substituting these values into the expression gives:
\[ \frac{1}{A} + \frac{1}{B} = \frac{A + B}{A \times B} = \frac{12}{35} \]

### Step 4: Conclusion
Thus, the sum of the reciprocals of the two numbers is:
\[ \frac{12}{35} \]

### Final Answer
The sum of the reciprocals of the two numbers is \( \frac{12}{35} \).

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