Question
Fill in the blank. If $A : B = 2 : 3$ and $B : C = 4 : 5$, then $C : A =$ ______.
✓
Answer
If $A : B = 2 : 3$ and $B : C = 4 : 5,$ then $C : A = 15 : 8.$
$\frac{\text{A}}{\text{C}}=\frac{\text{A}}{\text{B}}\times\frac{\text{B}}{\text{C}}$
$=\frac{2}{3}\times\frac{4}{5}=\frac{8}{15}$
$\therefore\text{C : A}=15:8$
$\frac{\text{A}}{\text{C}}=\frac{\text{A}}{\text{B}}\times\frac{\text{B}}{\text{C}}$
$=\frac{2}{3}\times\frac{4}{5}=\frac{8}{15}$
$\therefore\text{C : A}=15:8$
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