Discussion
If A : B = 2 : 3, B : C = 3 : 4 and C : D = 4 : 5, then the ratio of A : D is equal to:
Answer: B
A : D is 2 : 5. Multiply the chain of ratios so that B and C cancel:
\[ \frac{A}{D} = \frac{A}{B} \times \frac{B}{C} \]\[ \times \frac{C}{D} = \frac{2}{3} \times \frac{3}{4} \]\[ \times \frac{4}{5} = \frac{2}{5} \]5 : 2 is the inverse, and 2 : 3 and 5 : 7 do not follow from the three given ratios.
An equivalent method is to make B and C equal in both ratios: A : B = 2 : 3, B : C = 3 : 4 means A : B : C = 2 : 3 : 4, and C : D = 4 : 5 means A : B : C : D = 2 : 3 : 4 : 5. So A : D = 2 : 5, as the first method showed. The ratio 5 : 2 would be D : A.
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