It is proposed to build a single circular park equal in area to the sum of areas of
two circular parks of diameters 16 𝑚 and 12 𝑚 in a locality. The radius of the new park would be:

Area of the first circular park whose diameter is 16 m

$\begin{array}{r}=\pi r^2\\ =\pi (8{)}^2\\ =64\pi m^2\end{array}$

Area of the second circular park whose diameter is 12 m

$\begin{array}{r}=\pi r^2\\ =\pi (6{)}^2\\ =36\pi m^2\end{array}$

Let "R" be the radius of a single circular park 

Area of single park = area of first circular +area of second circular park

$\begin{array}{r}\pi R^2=64\pi +36\pi \\ \Rightarrow \pi R^2=100\pi \\ \Rightarrow R=10m\end{array}$

Therefore, the radius of the new park would be 10 𝑚
Hence, option (a) 10 𝑚 is correct.