A dealer professes to sell his goods at cost price but he uses a false weight of 950 grams for a kilogram. The gain percent of the dealer is (R.R.B., 2008)

### Concept & False Weight Gain Formula When goods are supposedly sold at cost price, any profit comes strictly from delivering less weight than claimed. The cost price corresponds to the actual weight given out, and the profit corresponds to the difference between claimed and actual weight. $$Gain\ \% = \left( \frac{Error}{True\ Weight - Error} \right) \times 100$$ ### Step-by-Step Solution * **True Weight:** 1 kilogram = 1000 grams. * **False Weight used:** 950 grams. * **Error in weight:** $1000 - 950 = 50$ grams. * The dealer invests in 950 grams but gets paid for 1000 grams. * **Gain \%** = $\left( \frac{50}{950} \right) \times 100$ * Gain \% = $\left( \frac{5}{95} \right) \times 100 = \left( \frac{1}{19} \right) \times 100$ * Gain \% = $\frac{100}{19}\% = 5 \frac{5}{19}\%$ ### Exam Strategy & Shortcut Memorize standard fraction-to-percentage conversions. The moment you see an error of 50g on a base of 950g, it simplifies to $\frac{1}{19}$. Knowing that $\frac{1}{19}$ is roughly $5.26\%$ immediately points to $5 \frac{5}{19}\%$. ### Common Pitfall A common trap is to divide the 50g error by the total 1000g, resulting in a false gain of 5%. Always use the substituted (false) weight as the denominator. ### Final Answer Therefore, the correct answer is **$5 \frac{5}{19}\%$**.