The medians CD and BE of a triangle ABC interest each other at O. The ratio of areas of $$\triangle$$ ODE : $$\triangle$$ ABC is equal to

$$\triangle$$ OED and $$\triangle$$ OCB are similar. We know that sides of similar triangles are in the same ratio.

OE : OB = 2 : 1

If two triangles are similar then the ratio of their areas is equal to the ratio of squares of their corresponding sides.

Equation can be written as,

$$\frac{OE^{2}}{OB^{2}} = \frac{Area\ of\ triangle\ ODE}{Area\ of\ triangle\ BCO}$$

Area of $$\triangle$$BCO = 4(Area of $$\triangle$$ ODE)

$$\frac{1}{3}$$ (Area of $$\triangle$$ ABC) = 4 (Area of triangle $$\triangle$$ ODE) ($$\because$$ area of  $$\triangle$$ BCO = $$\frac{1}{3}$$ area of $$\triangle$$ ABC)

Area of $$\triangle$$ ABC = 12 (Area of $$\triangle$$ ODE)

$$\triangle$$ ODE : $$\triangle$$ ABC = 1 : 12

Hence, option A is the correct answer.