Explanation

(a) $n_{A} = ?,\ n_{B} =$ Known frequency $= 320\ Hz$
$x = 4\ bps,$ which remains same after filing.
Unknown fork $A$ if filed so $n_{A} \uparrow$
Hence $n_{A} \uparrow - n_{B} = x\ \rightarrow Wrong$
$n_{B} - n_{A} \uparrow = x\ \rightarrow Correct$
$\Rightarrow \ n_{A} = n_{B} - x = 320 - 4 = 316\ Hz.$
This is the frequency before filing.
But in question after filing is asked which must be greater than $316\ Hz,$ such that it produces $4\ beats\ per\ sec.$ Hence it is $324\ Hz$