**D. 50 cm**

Area of first circle = πr^{2} = π(24)^{2} = 576π m^{2}

Area of second circle = πr^{2} = π(7)^{2} = 49π m^{2}

**Now, we are given that,**

Area of the circle = Area of first circle + Area of second circle

∴ πR^{2} = 576π +49π

**(where, R is the radius of the new circle)**

⇒ πR^{2} = 625π

⇒ R^{2} = 625

⇒ R = 25

∴ Radius of the circle = 25cm

**Thus, diameter of the circle = 2R = 50 cm.**