ABCD is a parallelogram, E and F are the midpoints of AB and CD respectively then the ratio of areas of AEFD and EBCF is ______.

As, ABCD is given parallelogram.
⇒ $\mathrm{AB}\parallel \mathrm{CD} \mathrm{and} \mathrm{AB}=\mathrm{CD}$
⇒ $\mathrm{AE}\parallel \mathrm{DF} \mathrm{and}\frac{1}{2}\mathrm{AB}=\frac{1}{2}\mathrm{CD}$
⇒ $\mathrm{AE}\parallel \mathrm{DF} \mathrm{and} \mathrm{AE}=\mathrm{DF}$

Therefore, AEFD is a parallelogram.

Similarly, EBCF is a parallelogram.
Now, AEFD and EBCF are parallelograms on equal bases and also between the same parallels, thus they have equal areas. 

⇒ Area of parallelogram AEFD : Area of parallelogram  EBCF = 1 : 1