Question

If $A:B=1:2,$ $B:C=3:4$ and $C:D=5:6,$ find $D:C:B:A$.

• A. $11:16:24:19$
• B. $48:40:30:15$
• C. $14:23:14:19$
• D. $32:17:16:15$

Answer 1

The correct option is B $48:40:30:15$

$\frac{A}{B}=\frac{1}{2}\Rightarrow A=\frac{1}{2}B,\frac{B}{C}=\frac{3}{4}\Rightarrow C=\frac{4B}{3}$

$\frac{C}{D}=\frac{5}{6}\Rightarrow D=\frac{6C}{5}=\frac{6}{5}\times \frac{4B}{3}=\frac{8B}{5}$

$\therefore D:C:B:A=\frac{8B}{5}:\frac{4B}{3}:B:\frac{B}{2}$

$=\frac{8B}{5}\times 30:\frac{4B}{3}\times 30:B\times 30:\frac{B}{2}\times 30=48:40:30:15$