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UPSC 2017 CDS II Math Paper
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© examsnet.com
Question : 56
Total: 100
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 ?
[2017 CDS-II]
12 cm and 5 cm
24 cm and 10 cm
60 cm and 25 cm
30 cm and 12.5 cm
Validate
Solution:
Let the diameters of the two circles be 12k cm and 5k cm.
∴
π
(
12
k
2
)
2
+
π
(
5
k
2
)
2
=
π
(
65
2
)
2
⇒
144
k
2
+
25
k
2
=
4225
⇒
169
k
2
=
4225
⇒
k
=
√
4225
169
=
√
25
=
5
c
m
Therefore, radius of one circle
=
12
×
5
2
=
30
c
m
Radius of the other circle
=
5
×
5
2
=
12.5
c
m
© examsnet.com
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