The sum and difference of a number with its reciprocal are `113/56 and 15/56` respectively, the number is :

Options

A. `11/4`
B. `13/6`
C. `14/8`
D. `7/8`

Answer

To solve the problem, we need to find a number \( a \) such that the sum and difference of the number and its reciprocal are given as \( \frac{113}{56} \) and \( \frac{15}{56} \) respectively.

### Step-by-Step Solution:

1. **Set Up the Equations**:
We know:
\[ a + \frac{1}{a} = \frac{113}{56} \quad \text{(1)} \]
\[ a - \frac{1}{a} = \frac{15}{56} \quad \text{(2)} \]

2. **Add the Two Equations**:
To eliminate \( \frac{1}{a} \), we can add equations (1) and (2):
\[ (a + \frac{1}{a}) + (a - \frac{1}{a}) = \frac{113}{56} + \frac{15}{56} \]
This simplifies to:
\[ 2a = \frac{113 + 15}{56} \]
\[ 2a = \frac{128}{56} \]

3. **Simplify the Right Side**:
We can simplify \( \frac{128}{56} \):
\[ 2a = \frac{128 \div 8}{56 \div 8} = \frac{16}{7} \]

4. **Solve for \( a \)**:
Now, divide both sides by 2:
\[ a = \frac{16}{7} \div 2 = \frac{16}{14} = \frac{8}{7} \]

5. **Conclusion**:
The number is:
\[ a = \frac{8}{7} \]