A farmer bought 749 sheep. He sold 700 of them for the price paid for the 749 sheep. The remaining 49 sheep were sold at the same price per head as the other 700. Based on the cost, the percent gain on the entire transaction is (M.B.A., 2010)

### Concept & Logic When a part of a stock is sold to exactly recover the total original cost, the remaining stock sold at the same rate represents pure profit. The profit percentage can be easily determined by comparing the number of "profit" units to the number of units required to break even. ### Step-by-Step Solution 1. Let the Cost Price (CP) of 1 sheep be $1. 2. Total CP for 749 sheep = $749. 3. The farmer sells 700 sheep for the total initial cost, meaning the Selling Price (SP) of 700 sheep = $749. 4. From this, the SP of 1 sheep = $\frac{749}{700} = $1.07. 5. The remaining 49 sheep are also sold at $1.07 each. 6. Total SP for all 749 sheep = $749 \times 1.07 = $801.43. 7. Total Profit = Total SP - Total CP = $801.43 - $749 = $52.43. 8. Profit % = $(\text{Profit} / \text{CP}) \times 100 = (\frac{52.43}{749}) \times 100 = 7\%$. ### Exam Strategy & Shortcut The sale of the first 700 sheep recovers the entire cost. This means the remaining 49 sheep are pure profit. The profit percentage is simply the ratio of the "profit sheep" to the "break-even sheep". Profit % = $(\frac{49}{700}) \times 100 = 7\%$. ### Common Pitfall Calculating the percentage based on the total number of sheep (749) instead of the base number of sheep required to break even (700). ### Final Answer Therefore, the correct answer is **7%**.