A shopkeeper purchased 150 identical pieces of calculators at the rate of ₹ 250 each. He spent an amount of ₹ 2500 on transport and packing. He fixed the labelled price of each calculator at ₹ 320. However, he decided to give a discount of 5% on the labelled price. What is the percentage profit earned by him?

### Concept & Total Cost Price and Profit Percentage The true Cost Price ($CP$) must include all overhead expenses like transport and packing. Profit percentage is always calculated on this total comprehensive Cost Price. $$Total CP = Base Price + Overheads$$ $$Profit \% = \left(\frac{SP - Total CP}{Total CP}\right) \times 100$$ ### Step-by-Step Solution * **Calculate the Total Cost Price (CP):** * Purchase cost = $150 \text{ calculators} \times 250 = 37500$ * Overhead expenses (transport/packing) = ₹ $2500$ * Total CP = $37500 + 2500 = 40000$ * **Calculate Total Selling Price (SP):** * Labelled price per calculator = ₹ $320$ * Discount = $5\%$ * Selling price per calculator = $320 \times \left(1 - \frac{5}{100}\right) = 320 \times 0.95 = 304$ * Total SP for 150 calculators = $150 \times 304 = 45600$ * **Calculate the Profit and Profit Percentage:** * Profit = Total SP - Total CP = $45600 - 40000 = 5600$ * Profit $\%$ = $\left(\frac{5600}{40000}\right) \times 100 = 14\%$ ### Exam Strategy & Shortcut Instead of finding the total values, find the per-item values to keep numbers small. CP per item = $250 + \left(\frac{2500}{150}\right) = 250 + 16.66 = \frac{800}{3}$ SP per item = $320 \times 0.95 = 304$ Ratio of SP to CP = $\frac{304}{\frac{800}{3}} = \frac{304 \times 3}{800} = \frac{912}{800} = \frac{114}{100} = 1.14$ A ratio of $1.14$ means exactly a $14\%$ profit. ### Common Pitfall Forgetting to add the transport and packing expenses (₹ $2500$) to the initial purchase price before calculating profit. This will give a falsely inflated profit percentage. ### Final Answer Therefore, the correct answer is **14%**.