If `(p-q)/(2)=3 and rp-rq=12`, then r=

Options

A. `-1`
B. `1`
C. `2`
D. `4`

Answer

To solve the equations given in the question, we will follow these steps:

1. **Start with the first equation**:
\[ \frac{p - q}{2} = 3 \]

2. **Multiply both sides by 2** to eliminate the fraction:
\[ p - q = 3 \times 2 \]
\[ p - q = 6 \]

3. **Now, consider the second equation**:
\[ rp - rq = 12 \]

4. **Factor out r from the left-hand side**:
\[ r(p - q) = 12 \]

5. **Substitute the value of \(p - q\) from step 2 into this equation**:
\[ r(6) = 12 \]

6. **Now, solve for r** by dividing both sides by 6:
\[ r = \frac{12}{6} \]
\[ r = 2 \]

Thus, the value of \(r\) is **2**.