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Answer

Let the radius of the bigger circle = r1

Let the radius of smaller circle = r2

Sum of the areas of both the circles = (22/7)*( r1^2 + r2^2) = 500.5 Sq.cm

Therefore r1^2 + r2^2 = (500.5)*(7/22) = 159.25

Now as both the circles touch each other internally,the distance between the centres is equal

to the difference of the radii.

That is r1- r2 = 3.5  cms…………………………………A

Now (r1 - r2)^2 = r1^2+r2^2 - 2r1r2

That is (3.5)^2 = 12.25 = 159.25 - 2r1r2

or 2r1r2 = 159.25 - 12.25 = 147

Now (r1+r2)^2 = r1^2+ r2^2 +2r1r2 = 159.25 +147 = 306.25

Therefore r1+r2 = (306.25)^0.5 = 17.5 …………….B

And r1- r2 = 3.5 …………………A

Solving ,we get r1 = 10.5 cms and r2 = 7cms

Therefore ratio between radii = r1/r2 = 10.5/7 = 1.5 = 3/2

Hence correct option = B    

 

Answer

Let the radius of the bigger circle be R and smaller circle radius be r. 

؞π(R^2+r^2)= 500.5= 1001/2 ..(i) and R-r=3.5=7/2..(ii)

=> 22/7(R^2+r^2)=1001/2=> (R^2+r^2)= 637/4 from (ii) R = r+7/2 => R^2 = r^2 + 7r + 49/4 putting it in (i) we get 

r^2 + 7r + 49/4 +r^2 = 637/4 => 2r^2 + 7r+ 49/4 = 637/4 => 8r^2 +28r-588 =0 => 2r^2 -14r +21r-147=0 => r=7, -21/2

Since radius can't be negative, discard-21/2 ؞ r=7  R= 7 +7/2=21/2. R/r = (21/2)/7= 21/14=3/2

hence option B is the correct answer

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