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

Let r₁ and r₂ be the radii of the two circles.

Given,

Sum of the radii of two circles is 140 cm.

r₁ + r₂ = 140 …….(1)

Circumference of circle₁ - Circumference of circle₂ = 88

⇒ 2πr₁ - 2πr₂ = 88

⇒ 2π(r₁ - r₂) = 88

⇒ r₁ - r₂ = $\dfrac{88}{2π}$

⇒ r₁ - r₂ = $\dfrac{88}{2 \times \dfrac{22}{7}}$

⇒ r₁ - r₂ = $\dfrac{88 \times 7}{2 \times 22}$

⇒ r₁ - r₂ = 14 ……….(2)

Adding equation (1) and (2), we get :

⇒ r₁ + r₂ + r₁ - r₂ = 140 + 14

⇒ 2r₁ = 140 + 14

⇒ 2r₁ = 154

⇒ r₁ = $\dfrac{154}{2}$

= 77 cm.

Substituting value of r₁ in equation (1), we get :

⇒ 77 + r₂ = 140

⇒ r₂ = 140 - 77

⇒ r₂ = 63 cm.

Hence, radii of the circles = 77 cm and 63 cm.