If a : b = 3 : 4 and b : c = 3 : 5 then a : c is:

The correct answer is Option (4) → 9 : 20

The two ratios share \(b\), so \(b\) is made the same in both before \(a\) and \(c\) are compared.

• \(a:b=3:4=9:12\) (multiplying by 3)

• \(b:c=3:5=12:20\) (multiplying by 4)

• So \(a:b:c=9:12:20\), and \(a:c=9:20\)

Shortcut: \(\displaystyle \frac{a}{c}=\frac{a}{b}\times\frac{b}{c}=\frac{3}{4}\times\frac{3}{5}=\frac{9}{20}\).