The owner of a milk store finds that, he can sell $980$ litres of milk each week at $₹14/$ litre and $1220$ litres of milk each week at $₹16$ litre. Assuming a linear relationship between selling price and demand, if $k$ litres could he sell weekly at $₹17 /$ litre then find the value of $k$.

Show that the points $P\left(-1.5, 3\right), Q\left(6, -2\right), R\left(-3, 4\right)$ are collinear.

If the area of the triangle formed by the vertices $A(-1, 2), B(k, -2)$ and $C(7, 4)$ (taken in order) is $22$ sq. units, find the value of $k$.

If the points $P\left(-1, -4\right), Q\left(b, c\right)$ and $R\left(5, -1\right)$ are collinear and $2b+c=4$, then find the values of $b$ and $c$.

The floor of a hall is covered with identical tiles which are in the shapes of triangles. One such triangle has the vertices $(-3, 2), (-1, -1)$ and $(1, 2)$. If the floor of the hall is completely covered by $110$ tiles, find the area of the floor.