The coordinates of the point P dividing the line

It is given that P divides the line segment joining the points A(1, 3) and B(4, 6) in the ratio 2 : 1.

Using section formula, we get

Coordinates of $\mathrm{P}=\left(\frac{2 \times 4+1 \times 1}{2+1}, \frac{2 \times 6+1 \times 3}{2+1}\right)=\left(\frac{9}{3}, \frac{15}{3}\right)=(3,5)$

Thus, the coordinates of P are (3, 5).

Hence, the correct answer is option B.