Solve the following :
In $\Delta PQR,NM||RQ$. If $PM=15,MQ=10,NR=8$, then find $PN$.

Given $NM||RQ$ and $PM=15,MQ=10,NR=8$

since $NM||RQ$ then by basic proportionality theorem

$\frac{PN}{NR}=\frac{PM}{MQ}$

$\frac{PN}{8}=\frac{15}{10}$

$PN=\frac{15}{10}\times 8$

$PN=\frac{3}{2}\times 8$

$\therefore PN=12$