A man bought some oranges at ₹ 10 per dozen and bought the same number of oranges at ₹ 8 per dozen. He sold these oranges at ₹ 11 per dozen and gained ₹ 120. The total number of oranges bought by him was

### Concept & Formula Set up an algebraic equation based on the total cost price, total selling price, and the absolute profit given in the problem to solve for the unknown quantity. $$\text{Total Profit} = \text{Total Selling Price} - \text{Total Cost Price}$$ ### Step-by-Step Solution * **Given:** CP1 = ₹ 10/dozen, CP2 = ₹ 8/dozen. Equal quantities bought. SP = ₹ 11/dozen. Total Gain = ₹ 120. * **Calculation:** 1. Let the number of dozens of oranges bought of each type be $x$. 2. Total number of dozens bought = $x + x = 2x$. 3. Total CP = $(10 \times x) + (8 \times x) = 10x + 8x = 18x$. 4. Total SP for all oranges = $11 \times (2x) = 22x$. 5. Gain = Total SP - Total CP = $22x - 18x = 4x$. 6. We are given that the total gain is ₹ 120. So, $4x = 120$. 7. $x = 30$. 8. The total number of oranges bought = $2x = 2 \times 30 = 60$ dozens. ### Exam Strategy & Shortcut Calculate profit per pair of dozens. Cost for 2 dozens (one of each type) = $10 + 8 = 18$. Selling price for these 2 dozens = $11 \times 2 = 22$. Profit on every 2 dozens = $22 - 18 = 4$. To get a total profit of 120, he needs $120 / 4 = 30$ such pairs. Total dozens = $30 \times 2 = 60$. ### Common Pitfall Solving for $x$ (which is 30) and hastily selecting option (a). The question asks for the **total** number of oranges bought, which is $2x$. ### Final Answer Therefore, the correct answer is **60 dozens**.