Initially beat frequency $=5 \mathrm{Hz}$

so, ${\rho }_{\mathrm{A}}=340\pm 5=345 \mathrm{Hz},$ or $335 \mathrm{Hz}$ 

after filing frequency increases slightly so, new value of frequency of $A>{\rho }_{\mathrm{A}}$

Now, beat frequency $=2 \mathrm{Hz}$

$\Rightarrow$ new ${\rho }_{\mathrm{A}}=340\pm 2=342 \mathrm{Hz},$ or $338 \mathrm{Hz}$

hence, original frequency of $A$ is ${\rho }_{\mathrm{A}}=335 \mathrm{Hz}$