Denominator of a number is `4` less than its numerator. If `6` is added to the numerator it becomes thrice the denominator. Find the fraction.

Options

A. `4/5`
B. `9/5`
C. `7/9`
D. `3/5`

Answer

To solve the problem step by step, we will define the variables and set up equations based on the information provided in the question.

### Step 1: Define the Variables
Let the numerator of the fraction be \( n \). According to the problem, the denominator is 4 less than the numerator. Therefore, we can express the denominator as:
\[ d = n - 4 \]

### Step 2: Set Up the Equation
The problem states that if 6 is added to the numerator, it becomes thrice the denominator. We can write this as:
\[ n + 6 = 3d \]
Substituting the expression for \( d \) from Step 1, we get:
\[ n + 6 = 3(n - 4) \]

### Step 3: Expand and Simplify the Equation
Now, let's expand the right side of the equation:
\[ n + 6 = 3n - 12 \]

### Step 4: Rearrange the Equation
Next, we will rearrange the equation to isolate \( n \):
1. Subtract \( n \) from both sides:
\[ 6 = 3n - n - 12 \]
2. This simplifies to:
\[ 6 = 2n - 12 \]
3. Now, add 12 to both sides:
\[ 6 + 12 = 2n \]
\[ 18 = 2n \]

### Step 5: Solve for \( n \)
Now, divide both sides by 2 to find \( n \):
\[ n = \frac{18}{2} = 9 \]

### Step 6: Find the Denominator
Now that we have \( n \), we can find the denominator \( d \):
\[ d = n - 4 = 9 - 4 = 5 \]

### Step 7: Write the Fraction
Now we can write the fraction:
\[ \text{Fraction} = \frac{n}{d} = \frac{9}{5} \]

### Final Answer
The required fraction is:
\[ \frac{9}{5} \]

---