If the sum of the diameters of two circles is 30 cm and the difference of their radii is 5 cm, then the ratio of area of the smaller circle to that of the bigger circle is:

1 : 4

We have,

The sum of the diameters of two circles is 30 cm and the difference of their radii is 5 cm.

Let the radii of two circles = R and r

According to the question,

D + d = 30

So, R + r = 15

and R - r = 5

so, R = ( 15 + 5 ) /2 = 10

and r = 5

So, The ratio of area of smaller circle to the bigger circle = r² : R²

= 5² : 10²

= 25 : 100 = 1 : 4