Let tension be $T$

$f_1=\sqrt{\frac{T}{\mu}} \times \frac{1}{2 l}=256$

$f_2=\sqrt{\frac{T+10}{\mu}} \times \frac{1}{2 l}=320$

$\sqrt{\frac{T}{T+10}}=\frac{256}{320}$

$\frac{T}{T+10}=\frac{(16)^2}{(16)^2 \times(20)^2}$

or $\frac{T}{T+10}=\frac{16^2}{(20)^2}$

or $400 T=256 T^2+2560$

or $144 T=2560$

or $T=\frac{2560}{144}$

or $T=\frac{2560}{16 \times 9}$

or $T=\frac{160}{9}$ Newton

$=\frac{16}{9} \,kg -w t$