$\mathrm{p}, \mathrm{q}, \mathrm{r}, \mathrm{s}, \mathrm{m}, \mathrm{n}$ be the position vectors of points $\mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S}, \mathrm{M}, \mathrm{N}$.
Now $\overline{\mathrm{PS}}+\overline{\mathrm{QR}}$
$$
=\overline{\mathrm{s}}-\overline{\mathrm{p}}+\overline{\mathrm{r}}-\overline{\mathrm{q}}=(\overline{\mathrm{s}}+\overline{\mathrm{r}})-(\overline{\mathrm{p}}+\overline{\mathrm{q}})
$$
Since $\mathrm{M}$ and $\mathrm{N}$ are mid-points of PQ and RS respectively, we write
$\overline{\mathrm{m}}=\frac{\overline{\mathrm{p}}+\overline{\mathrm{q}}}{2}$ and $\overline{\mathrm{n}}=\frac{\overline{\mathrm{r}}+\overline{\mathrm{s}}}{2}$
$\therefore$ eq. (1) becomes
$$
\overline{\mathrm{PS}}+\overline{\mathrm{QR}}=2 \overline{\mathrm{n}}-2 \overline{\mathrm{m}}=2(\overline{\mathrm{n}}-\overline{\mathrm{m}})=2 \overline{\mathrm{MN}}
$$
From given data, $\mathrm{t}=2$