If x and y are positive integer numbers and `(3x)/(y)=6` then find the minimum value of `3x-4y`.

Options

A. 2
B. 1
C. 6
D. 8

Answer

To solve the problem, we need to find the minimum value of \(3x - 4y\) given the equation \(\frac{3x}{y} = 6\) where \(x\) and \(y\) are positive integers.

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ \frac{3x}{y} = 6 \]
This can be rewritten as:
\[ 3x = 6y \]
Dividing both sides by 3 gives:
\[ x = 2y \]

2. **Substitute \(x\) in the expression \(3x - 4y\):**
We need to find the minimum value of:
\[ 3x - 4y \]
Substituting \(x = 2y\) into the expression:
\[ 3(2y) - 4y = 6y - 4y = 2y \]

3. **Minimize \(2y\):**
Since \(y\) is a positive integer, the smallest value \(y\) can take is 1. Therefore:
\[ 2y = 2 \times 1 = 2 \]

4. **Conclusion:**
The minimum value of \(3x - 4y\) is:
\[ \boxed{2} \]