Question

Point B is on line AC so that AB : BC = 2 : 1. Point D is on line AB so that AD : DB = 3 : 2. Find AD : DC

Answer 1

Firstly, we will draw figure

Let's assume

length of AC=x

we have

AB : BC = 2 : 1

so,

$AB=\frac{2}{3} x$

$BC=\frac{1}{3} x$

Point D is on line AB

and

$AB=\frac{2}{3} x$

AD : DB = 3 : 2

so, we get

$AD=\frac{3}{5} *\frac{2}{3} x$

$AD=\frac{2}{5} x$

$DB=\frac{2}{5} *\frac{2}{3} x$

$DB=\frac{4}{15} x$

now, we can locate these values

Firstly, we will find DC

DC=DB+BC

now, we can plug values

$DC=\frac{4}{15} x+\frac{1}{3} x$

$DC=\frac{3x}{5}$

we have got

$AD=\frac{2}{5} x$

now, we can find ratio

$\frac{AD}{DC} =\frac{\frac{2}{5} x}{\frac{3x}{5}}$

now, we can simplify it

$\frac{AD}{DC} =\frac{2}{3}$

so,

AD:DC=2:3...........Answer