A shopkeeper purchased 70 kg of potatoes for ₹ 420 and sold the whole lot at the rate of ₹ 6.50 per kg. What will be his gain percent? (S.S.C., 2007)

### Concept & Unit Price Method Instead of calculating the total Selling Price for all items, it is often faster to find the Cost Price and Selling Price of a single unit. The gain percentage remains the same regardless of quantity. $$ \text{Gain \%} = \left( \frac{\text{SP per unit} - \text{CP per unit}}{\text{CP per unit}} \right) \times 100 $$ ### Step-by-Step Solution Given: * Total Cost Price (CP) for 70 kg = ₹ 420 * Selling Price (SP) per kg = ₹ 6.50 Calculation: 1. Find the Cost Price (CP) of 1 kg of potatoes. $$ \text{CP per kg} = \frac{420}{70} = 6 $$ 2. Calculate the gain per kg. $$ \text{Gain} = \text{SP per kg} - \text{CP per kg} = 6.50 - 6 = 0.50 $$ 3. Calculate the gain percentage based on the CP per kg. $$ \text{Gain \%} = \left(\frac{0.50}{6}\right) \times 100 $$ 4. Simplify the expression. $$ \text{Gain \%} = \frac{50}{6} = \frac{25}{3} $$ 5. Convert the improper fraction to a mixed fraction. $$ \frac{25}{3} = 8\frac{1}{3}\% $$ ### Exam Strategy & Shortcut By identifying the per-unit costs quickly ($420/70 = 6$), you see the ratio of profit to cost is $0.5/6$, which is $1/12$. Memorizing standard fraction-to-percentage conversions ensures you know $1/12 = 8\frac{1}{3}\%$ instantly, saving calculation time. ### Common Pitfall A common mistake is calculating the total Selling Price ($70 \times 6.50 = 455$), which adds an unnecessary multiplication step that increases the chance of a calculation error before finding the difference ($455 - 420 = 35$). Both methods work, but per-unit is faster. ### Final Answer Therefore, the correct answer is **$8\frac{1}{3}\%$**.