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

Given:

The sum of the radii of two circles is 140 cm and the difference of their circum­ferences is 88 cm.

To do:

We have to find the diameters of the circles.

Solution:

Let the radius of the two circles be $r_1$ and $r_2$.

We know that,

Circumference of a circle of radius $r=2 \pi r$

Therefore,

The sum of the radii of two circles $=140\ cm$.

$r_1+r_2=140$..............(i)

The difference of the circum­ferences of two circles $=88\ cm$.

$2\pi r_1-2\pi r_2=88$

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

$r_1-r_2=2(7)$

$r_1-r_2=14$...........(ii)

Adding equations (i) and (ii), we get,

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

$2r_1=154$

$r_1=77\ cm$

$\Rightarrow r_2=140-77=63\ cm$

$\Rightarrow d_1=2r_1=2(77)=154\ cm$

$\Rightarrow d_2=2r_2=2(63)=126\ cm$

The diameters of the circles are $154\ cm$ and $126\ cm$.