If $\text{A:B}=3:4$ , $\text{B:C}=5:7$ , $\text{C:D}=8:9$ then $\text{A:D}=$

L.C.M of $\text{4},\text{5}=20$

$\text{A:B}=\left(3:4\right)\times 5=15:20$

$\text{B:C}=\left(5:7\right)\times 4=20:28$

$\text{C:D}=\left(8:9\right)\times \frac{7}{2}=28:\frac{63}{2}$

$A:B:C:D=15:20:28:\frac{63}{2}$

$A:B:C:D=\frac{15\times 2}{2}:\frac{20\times 2}{2}:\frac{28\times 2}{2}:\frac{63}{2}=30:40:56:63$

$\therefore \text{A:D}=30:63$

           $=10:21$