If the line $2x + y = k$ passes through the point which divides the line segment joining the points (1,1) and (2,4) in the ratio 3:2, then $k$ equals

If P $(x,y)$ divides the line segment $AB$in the ratio 3:2, then 

$x=\frac{3\left(2\right)+2\left(1\right)}{5},y=\frac{3\left(2\right)+2\left(1\right)}{5}$

         $P(8 / 5,14 / 5)$

As the line $2x + y = k$ passes through $P$

$2\times (8/5)+(14/5)=k\Rightarrow k=6$