If \((4a-3b):(5a-2b)=3:4\), then \(a:b\) is equal to:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 6 : 1
Two equal ratios can be cross-multiplied: if \(p:q=r:s\), then \(ps=qr\).
\(\displaystyle \frac{4a-3b}{5a-2b}=\frac{3}{4}\)
\(4(4a-3b)=3(5a-2b)\)
\(16a-12b=15a-6b\)
\(a=6b\)
\(a:b=6:1\)
Check with \(a=6,\ b=1\): \(4a-3b=21\), \(5a-2b=28\), and \(21:28=3:4\)
So \(a:b=\) 6 : 1.