A fraction is such that the numerator is five less than the denominator. Also four times the numerator is one more than the denominator. The fraction is:
एक भिन्न इस प्रकार है कि अंश , हर से 5 कम है | साथ ही, अंश का चार गुना हर से एक अधिक है | यह भिन्न है :

Options

A. `4/7`
B. `3/8`
C. `7/12`
D. `2/7`

Answer

To solve the problem step by step, we will define the variables for the numerator and denominator, set up equations based on the given conditions, and solve for the values.

### Step-by-Step Solution:

1. **Define the Variables**:
Let the numerator be \( x \) and the denominator be \( y \).

2. **Set Up the First Equation**:
According to the problem, the numerator is five less than the denominator. This can be expressed as:
\[ x = y - 5 \quad \text{(Equation 1)} \]

3. **Set Up the Second Equation**:
The problem also states that four times the numerator is one more than the denominator. This can be expressed as:
\[ 4x = y + 1 \quad \text{(Equation 2)} \]

4. **Substitute Equation 1 into Equation 2**:
We can substitute the value of \( x \) from Equation 1 into Equation 2:
\[ 4(y - 5) = y + 1 \]

5. **Expand and Simplify**:
Expanding the left side gives:
\[ 4y - 20 = y + 1 \]
Now, we will move \( y \) to the left side and the constant to the right side:
\[ 4y - y = 20 + 1 \]
Simplifying this gives:
\[ 3y = 21 \]

6. **Solve for \( y \)**:
Dividing both sides by 3:
\[ y = 7 \]

7. **Find \( x \)**:
Now that we have \( y \), we can find \( x \) using Equation 1:
\[ x = y - 5 = 7 - 5 = 2 \]

8. **Write the Fraction**:
The fraction is given by:
\[ \frac{x}{y} = \frac{2}{7} \]

### Final Answer:
The fraction is \( \frac{2}{7} \).

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