If point $P$ divides the line joining the points $(5,0)$ and $(0,4)$ in the ratio $2:3$ internally, then the $x$ coordinate of $P$ is

The correct option is C: $3$

The point $P(X,Y)$ divides the line joining the points $A(5,0)$ and

$B(0,4)$ in the ratio $m:n$

$(x_1=5,y_1=0)$ and $(x_2=0,y_2=4)$

and $m=2,n=3$

By Section formula, the coordinates of $P$ will be $x=\frac{m{x}_2+n{x}_1}{m+n},y=\frac{m{y}_2+n{y}_1}{m+n}$

$\therefore$ The abscissa of $P$ is $x=\frac{m{x}_2+n{x}_1}{m+n}=\frac{2\times 0+3\times 5}{2+3}=3$