PQRS is a rectangle in which PQ $\text{=}$  2PS. T and U are the mid points of PS and PQ respectively. QT and US intersect at V. The area of QRSV divided by the area of PQT is

In PQRS

$\left[\Delta PQT\right]=\frac{1}{2}\times TP\times PQ$

$=\frac{1}{2}\times \frac{1}{2}\times 2TP\times PQ$

$=\frac{1}{4}\times SP\times PQ=\frac{1}{4}\times \left[PQRS\right]$   $\left(\because TP=\frac{SP}{2},SP\times PQ=\left[PQRS\right]\right)$

$\therefore \left[\Delta PQT\right]=\frac{1}{4}\times \left[PQRS\right]$

$\left[QRSV\right]=\left[\Delta QRS\right]+\left[\Delta SVQ\right]$

$\left[\Delta QRS\right]=\frac{\left[PQRS\right]}{2}$ (Diagonal divides rectangle into two equal area parts )

$\left[\Delta SVQ\right]=\frac{1}{3}\times \left[\Delta PSQ\right]$     $\left(\because Viscentroid\right)$

$=\frac{1}{3}\times \frac{1}{2}\left[PQRS\right]=\frac{\left[PQRS\right]}{6}$

$\left[QRSV\right]=\frac{\left[PQRS\right]}{2}+\frac{\left[PQRS\right]}{6}=\frac{2}{3}\left[PQRS\right]$

$\frac{\left[QRSV\right]}{\left[PQT\right]}=\frac{\frac{2}{3}\times \left[PQRS\right]}{\frac{1}{4}\times \left[PQRS\right]}=\frac{8}{3}$