Official solution
The point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2 is
\[ = \left( {{{3 \times 2 + 2 \times 1} \over {3 + 2}},{{3 \times 4 + 2 \times 1} \over {3 + 2}}} \right)\]
\[ = \left( {{{6 + 2} \over 5},{{12 + 2} \over 5}} \right) = \left( {{8 \over 5},{{14} \over 5}} \right)\]
Since the line 2x + y = k passes through this point,
\[\therefore\] \[2 \times {8 \over 5} + {{14} \over 5} = k\] or \[{{30} \over 5} = k\] or, k = 6