Question

The sum of the radii of two circles is $140cm$ and the difference of the circumferences is $88cm$. Find the diameters of the circles.

Answer 1

Let $r_1$ and $r_2$ be the radii of two given circles.

So, $r_1+r_2=140cm$ ........(1)

Also, $2\pi r_1-2\pi r_2=88cm$

$\Rightarrow 2\pi (r_1-r_2)=88cm$

$\Rightarrow 2\times \frac{22}{7}(r_1-r_2)=88cm$

$\Rightarrow r_1-r_2=\frac{7}{22\times 2}\times 88cm$

$\Rightarrow r_1-r_2=7\times 2cm$

$\Rightarrow r_1-r_2=14cm$ ........(2)

Lets add (1) and (2), we get

$r_1+r_2+r_1-r_2=140cm+14cm$

$\Rightarrow 2r_1=154cm$

$\Rightarrow d_1=154cm$ [$\because d_1=2r_1$]

Lets do (1) $-$ (2), we get

$r_1+r_2-r_1+r_2=140cm-14cm$

$\Rightarrow 2r_2=126cm$

$\Rightarrow d_2=126cm$ [$\because d_2=2r_2$]

So, the diameters are $154cm$ and $126cm$.