If \((5a-3b):(4a-2b)=2:3\), then \(a:b\) is equal to:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 5 : 7
Write the ratio as two equal fractions and cross-multiply; then collect the \(a\) terms on one side and the \(b\) terms on the other.
\(\displaystyle \frac{5a-3b}{4a-2b}=\frac{2}{3}\)
\(3(5a-3b)=2(4a-2b)\)
\(15a-9b=8a-4b\)
\(7a=5b\)
\(\displaystyle \frac{a}{b}=\frac{5}{7}\)
So \(a:b=\) 5 : 7.