Question 757750
the angle bisector of an angle of the triangle divides the opposite side with a ratio proportionate to corresponding sides
so here 
Bd/CD=AB/Ac .........1
now the ratio of areas=ABD/ACD=[(1/2)BD*h]/[(1/2)CD*h]   {h=height of the triangles being same for same vertex}
so ABD/ACD=BD/CD=AB/Ac=16/24=2/3 (use eqn 1 above)