A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was 

Suppose n_P = frequency of piano = ?  $({\mathrm{n}}_{\mathrm{P}}\propto \sqrt{\mathrm{T}})$
n_f = Frequency of tuning fork = 256 Hz
x = Beat frequency = 5 bps, which is decreasing (5$\to$2) after clanging the tension of piano wire 
Also, tension of piano wire is increasing so n_P$\downarrow$
Hence n_P$\uparrow$– n_f = x$\downarrow$      $\to$       Wrong 
          n_f – n_P$\uparrow$= x$\downarrow$       $\to$      Correct 
$\Rightarrow$ n_P = n_f – x = 256 – 5 Hz.