If \((3a-2b):(4a-b)=5:7\), then \(a:b\) is equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 9 : 1
Two equal ratios can be cross-multiplied: if \(p:q=r:s\), then \(ps=qr\).
\(\displaystyle \frac{3a-2b}{4a-b}=\frac{5}{7}\)
\(7(3a-2b)=5(4a-b)\)
\(21a-14b=20a-5b\)
\(a=9b\)
\(a:b=9:1\)
Check with \(a=9,\ b=1\): \(3a-2b=25\), \(4a-b=35\), and \(25:35=5:7\)
So \(a:b=\) 9 : 1.