Question

Four points are on a line segment, as shown. If $AB:BC=1:2$ and $BC:CD=8:5$, find $AB:BD$.

• A. $4:13$
• B. $1:13$
• C. $1:7$
• D. $3:13$

Answer 1

The correct option is A $4:13$

Shown that four points are on a line segment,

$AB:BC=1:2$

$BC:CD=8:5$

$\Rightarrow$ AB:BD=?

As $AB:BC=4:8$ $[4\times (1:2\left)\right]$

Both ratios express $BC$ are unit $8$,

$AB:BC:CD=4:8:5$

$\Rightarrow$ AB : BD = 4 : (8+5)

$=4:13$