If A : B = 3 : 5, B : C = 8 : 9 and C : D = 15 : 4, then find A : D.

The correct answer is Option (3) → 2 : 1

The ratios form a chain A to B to C to D, so multiplying them cancels B and C and leaves A to D: \(\displaystyle \frac{A}{D}=\frac{A}{B}\times\frac{B}{C}\times\frac{C}{D}\).

• \(\displaystyle \frac{A}{D}=\frac{3}{5}\times\frac{8}{9}\times\frac{15}{4}=\frac{360}{180}=2\)

• A : D \(=2:1\)