ABCD is a trapezium in which AB || DC and its diagonals intersect at P. If AP = (3x - 1) cm. PC = (5x - 3) cm. BP = (2x + 1) cm and PD = (6x - 5) cm, then the length of DB is:

Answer: Option B

$$\begin{array}{rl}& \frac{\text{AP}}{\text{PC}}=\frac{\text{BP}}{\text{PD}}\left(\text{Similarity}\right)\\ & \frac{3\text{x}-1}{5\text{x}-3}=\frac{2\text{x}+1}{6\text{x}-5}\end{array}$$
18x² - 6x - 15x + 5 = 10x² + 5x - 6x - 3
8x² - 20x + 8 = 0
x = 2, $$\frac{1}{2}$$
at x = 2,
DB = 6x - 5 + 2x + 1
= 8x - 4
= 8 × 2 - 4
= 12