Question

A segment $AB$ is divided at point $P$ Such that $\frac{PB}{NB}=\frac{3}{7},$ then find the ratio $AP:PB$

Answer 1

$\frac{PB}{AB}=\frac{3}{7}\to \left(1\right)\Rightarrow \frac{(AB-AP)}{AB}=\frac{3}{7}\Rightarrow 7(AB-AP)=3AB\Rightarrow 7AB-3AB=7AP\Rightarrow 4AB=7AP\frac{AP}{AB}=\frac{4}{7}\to \left(2\right)$

From $\left(1\right)$ and $\left(2\right)$

$\frac{AP}{AB}÷\frac{PB}{AB}=\frac{4}{7}÷\frac{3}{7}\Rightarrow \frac{AP}{PB}=\frac{4}{3}\Rightarrow AP:PB=4;3$