A shopkeeper sells his items using a faulty balance which measures 25% less. He then marks up his items 15% above the cost price. If he also gives a discount of 10%, then find his net profit percentage on 1 kg items

$$\eqalign{ & \frac{{MP}}{{CP}} = \frac{{115}}{{100}} \cr & \frac{{MP}}{{CP}} = \frac{{100 + P}}{{100 - d}}\,\,\,\,\left( {d\% = 10\% } \right) \cr & \Rightarrow \frac{{115}}{{100}} = \frac{{100 + P}}{{100 - 10}} \cr & \Rightarrow \frac{{23}}{{20}} = \frac{{100 + P}}{{90}} \cr & \Rightarrow P\% = 3.5\% \cr & {\text{Now, According to the question he weights }}25\% {\text{ less}} \cr & 25\% = \frac{1}{4} \cr & \frac{{SP}}{{CP}} = \frac{4}{3} \times \frac{{103.5}}{{100}} = \frac{{69}}{{50}} \cr & {\text{Profit }}\% = \frac{{19}}{{50}} \times 100 = 38\% \cr} $$