In the figure, the radius of each of the two smallest circles(S) is one-fifth of the largest circle. The radius of the middle sized circle (M) is double that of the smallest circle. What fraction of the large circle is shaded?

Let us consider the radius of the biggest circle as 5r.

This makes the radius of the two smallest circles as r, and the middle sized circle as 2r.

Now, we shall calculate the total area of the bigger circle. It shall be $$\pi$$ $$(5r)^{2}$$, which is 25$$\pi$$ $$r^{2}$$. Let us say the area is 25x units.

For the two smaller circles, the total area is 2$$\pi$$ $$r^{2}$$.

And the middle sezied circle's area is $$\pi$$ $$(2r)^{2}$$, which is 4$$\pi$$ $$r^{2}$$.

Now, we shall add the area of two smallest circles with the middle sized circle and subtract it from the area of the bigger circle to find the area which is shaded.

The sum of shaded region is 6$$\pi$$ $$r^{2}$$. Let us say that the sum is 6x units. 

Hence, the part of bigger circle which is not shaded becomes 19x units. 

Now, the ratio of area shaded to the ratio of area of the bigger circle is 19:25.