A grocer professes to sell goods at the cost price but uses false weights. He gains $$\frac{{100}}{9}$$% in this manner. He uses a weight of

$$\eqalign{ & {\text{Gain}}\% \cr & = {\frac{{ {{\text{True}}\,{\text{Weight}} - {\text{False}}\,{\text{Weight}}} }}{{{\text{False}}\,{\text{Weight}}}}} \times 100 \cr & \frac{{100}}{9} = {\frac{{ {1 - x} }}{x}} \times 100 \cr & \frac{{ {1 - x} }}{x} = \frac{1}{9} \cr & 10x = 9 \cr & x = 0.9\,kg = 900\,gms \cr} $$