If a:b=c:d=e:f then (pa+qc+re):(pb+qd+rf) is equal to

Answer

To solve the problem, we start with the given ratio \( a:b = c:d = e:f \). Let's denote this common ratio as \( k \).

1. **Express each variable in terms of the common ratio \( k \)**:
- From \( a:b = k \), we can express \( a \) as \( a = bk \).
- From \( c:d = k \), we can express \( c \) as \( c = dk \).
- From \( e:f = k \), we can express \( e \) as \( e = fk \).

2. **Substitute these expressions into the ratio we need to find**:
We need to find the ratio \( (pa + qc + re):(pb + qd + rf) \).
- Substitute \( a \), \( c \), and \( e \):
\[ (pa + qc + re) = (p(bk) + q(dk) + r(fk)) = k(pb + qd + rf) \]

3. **Now, substitute into the denominator**:
The denominator is already given as \( (pb + qd + rf) \).

4. **Combine the results**:
Now we have:
\[ \frac{(pa + qc + re)}{(pb + qd + rf)} = \frac{k(pb + qd + rf)}{(pb + qd + rf)} \]

5. **Simplify the expression**:
Since \( (pb + qd + rf) \) is common in both the numerator and the denominator, we can cancel it out (assuming \( pb + qd + rf \neq 0 \)):
\[ = k \]

6. **Final result**:
Thus, we find that the ratio \( (pa + qc + re):(pb + qd + rf) \) is equal to \( k:1 \).

### Final Answer:
The final answer is \( k:1 \).