A man buys eggs at 2 for ₹ 1 and an equal number at 3 for ₹ 2 and sells the whole at 5 for ₹ 3. His gain or loss percent is

### Concept & Formula When an equal number of items are bought at two different rates, the best approach is to assume a total quantity that is a multiple of all given item quantities (Lowest Common Multiple). $$Profit \% = \left( \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \right) \times 100$$ ### Step-by-Step Solution * **Given:** CP1 = 2 eggs for ₹ 1. CP2 = 3 eggs for ₹ 2. SP = 5 eggs for ₹ 3. * **Calculation:** 1. Find the LCM of the quantities (2, 3, and 5), which is 30. 2. Let the man buy 30 eggs of the first kind and 30 eggs of the second kind. Total eggs bought = 60. 3. CP of first 30 eggs = $\frac{1}{2} \times 30 = \text{₹ } 15$ 4. CP of second 30 eggs = $\frac{2}{3} \times 30 = \text{₹ } 20$ 5. Total CP for 60 eggs = $15 + 20 = \text{₹ } 35$ 6. SP of all 60 eggs = $\frac{3}{5} \times 60 = 3 \times 12 = \text{₹ } 36$ 7. Since SP > CP, there is a gain. Gain = $36 - 35 = \text{₹ } 1$ 8. Gain \% = $\left( \frac{1}{35} \right) \times 100 = \frac{100}{35} = \frac{20}{7} = 2\frac{6}{7}\%$ ### Exam Strategy & Shortcut By using the LCM of the quantities involved (2, 3, 5 = 30), you avoid fractional math entirely. Always calculate the total cost and total selling price for this assumed bulk amount to find the exact net profit or loss directly. ### Common Pitfall A frequent error is averaging the two cost prices per egg directly, leading to an incorrect total CP baseline. You must sum the total cost of equal batches. ### Final Answer Therefore, the correct answer is **$2\frac{6}{7}$% gain**.