To get the ratio p:q (for `p ne q`) one has to add a number to each term of the ratio x: y, the number is:

Options

A. `(px + qy)/(p-q)`
B. `(qx - py)/(p-q)`
C. `(px- qy)/(p-q)`
D. `(py-qx)/(p-q)`

Answer

To find the number that needs to be added to each term of the ratio \(x:y\) to obtain the ratio \(p:q\) (where \(p \neq q\)), we can follow these steps:

### Step-by-Step Solution:

1. **Set Up the Equation**:
We start with the ratio \(x:y\) and want to add a number \(A\) to both terms. This gives us the new ratio \((x + A):(y + A)\).

2. **Express the New Ratio**:
We want this new ratio to equal \(p:q\). Therefore, we can write the equation:
\[ \frac{x + A}{y + A} = \frac{p}{q} \]

3. **Cross-Multiply**:
To eliminate the fraction, we cross-multiply:
\[ (x + A)q = (y + A)p \]

4. **Expand the Equation**:
Expanding both sides gives:
\[ xq + Aq = yp + Ap \]

5. **Rearrange the Equation**:
We can rearrange the equation to isolate terms involving \(A\):
\[ Aq - Ap = yp - xq \]

6. **Factor Out \(A\)**:
Factoring \(A\) from the left side, we have:
\[ A(q - p) = yp - xq \]

7. **Solve for \(A\)**:
Finally, we can solve for \(A\) by dividing both sides by \((q - p)\):
\[ A = \frac{yp - xq}{q - p} \]

### Final Answer:
The number that needs to be added to each term of the ratio \(x:y\) to obtain the ratio \(p:q\) is:
\[ A = \frac{yp - xq}{q - p} \]