If a:b=c:d=e:f=5:7, then what is the ratio (3a+5c+11e):(3b+5d+11f)?
A. 11 : 7
B. 3 : 7
C. 7 : 11
D. 5 : 7 (Correct answer)
Correct Answer
Option D — 5 : 7
Detailed Solution & Explanation
The correct answer is 5 : 7.
Key Points
When several ratios are equal ($\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\frac{5}{7}$), any weighted combination of numerators over the same combination of denominators keeps the ratio.
So $(3a+5c+11e):(3b+5d+11f)=5:7$.
Additional Information
If a/b = c/d = e/f = k, then any combination (pa + qc + re)/(pb + qd + rf) also equals k, whatever the weights p, q and r.
This follows because each numerator is k times its matching denominator, so k factors straight out of the sum.
The weights 3, 5 and 11 are therefore irrelevant — recognising that turns the question into a one-line answer.