The sum of the radii of two circle is $140 c m$ and the difference of their circumference is 88 cm. Find the radii of the two circles.

77 c m

63 c m

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35 c m

105 c m

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75 c m

65 c m

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55 c m

85 c m

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Solution

The correct option is A $77 c m$ , $63 c m$
Let the radii of the two circles be $r_{1}$ and $r_{2}$
Given, $r_{1} + r_{2} = 140$
$⟹ r_{1} = 140 - r_{2}$ --------(i)

Also, $2 π r_{1} - 2 π r_{2} = 88$
$⟹ r_{1} - r_{2} = \frac{88}{2 π}$

Putting the value of $r_{1}$ from equation (i), we have

$⟹ 40 - r_{2} - r_{2} = \frac{88 \times 7}{2 \times 22}$

$⟹ 2 r_{2} = 140 - 14$

$⟹ r_{2} = 63$

Putting the value of $r_{2}$ in (i), we get
$⟹ r_{1} = 140 - 63$
$⟹ r_{1} = 77$

Thus, the two radii are $77$ cm and $63$ cm.

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