The diameters of two given circles are in the ratio 12 5 and the sum of their areas is equal to the ...........

Quantitative Aptitude (CDS) Mensuration 2D

The diameters of two given circles are in the ratio 12:5 and the sum of their areas is equal to the area of a circle of diameter 65 cm. What are their radii?

12 cm and 5 cm

24 cm and 10 cm

60 cm and 25 cm

30 cm and 12.5 cm

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Explanation:

Let the radius of two circle are 12r and 5r
And, sum of area of two circles = $\pi$ (12r)²+ $\pi$ (5r)²
Area of circles whose diameter is 65 cm = $\pi$ (65/2)²
According to question,
$\pi$ (144r²)+ $\pi$ (25r²)= $\pi$ (4225/4)
=>169r²=(4225/4)=>r²=4225/(4×169)
=>r= 65/26=5/2
Hence radius of the circles are (12×52)=30 cm and (5×52)=12.5cm