Let the total number of items in the man's shop = \(y\)

Number of Brand A's items in the man's shop = \(\frac {1}{9} y\)

Remaining items = 1 - \(\frac {1}{9} y = \frac {8}{9} y\)

Number of Brand B's items in The man's shop = \(\frac{5}{8} of \frac{8}{9}y = \frac{5}{9}y\)

Total of Brand A and Brand B's items = \(\frac{1}{9}y + \frac{5}{9}y = \frac{2}{3}y\)

Number of Brand C's items in the man's shop = 1 - \(\frac{2}{3}y = \frac{1}{3}y\)

\(\implies\frac{1}{3}y\) = 81 (Given)

\(\implies y\) = 81 x 3 = 243

∴ The total number of items in the man's shop = 243

∴ Number of Brand B's items in the man's shop = \(\frac{5}{9}\) x 243 = 135

∴ The number of more Brand B items than Brand C = 135 - 81 =54