A trader professes to sell his goods at a nominal gain percentage but actually earns $$37\frac{1}{2}$$% profit by using false weight. If for a kg he uses a weight of 800 gm, what is the nominal gain percentage at which he claims to be selling his goods ?

Let the required gain be x%
Percentage deduction in weight
$$\eqalign{ & = \left( {\frac{{200}}{{1000}} \times 100} \right)\% \cr & = 20\% \cr & \therefore \frac{{20 + x}}{{100 - 20}} \times 100 = 37\frac{1}{2} \cr & \Rightarrow \frac{{20 + x}}{{80}} = \frac{3}{8} \cr & \Rightarrow 20 + x = 30 \cr & \Rightarrow x = 10 \cr} $$
Hence, nominal gain percentage = 10%