(c) After filling frequency increases, so $n_{A}$ increases $( \uparrow ).$ Also it is given that beat frequency increases ($i.e.,\ x \uparrow$)
Hence $n_{A} \uparrow - n_{B} = x \uparrow \ \ \ \ \rightarrow$ Correct …(i)
$n_{B} - n_{A} \uparrow = x \uparrow \ \ \ \ \rightarrow$ Wrong …(ii)
$\Rightarrow n_{A} = n_{B} + x = 512 + 5 = 517\ Hz$