Profit, Loss and Discount

To gain 20% on a cost of 300, the selling price must be 300 * 1.20 = 360. If the discount is 4%, then 360 = Marked Price * (1 - 0.04), so Marked Price = 360 / 0.96 = 375.

Profit = 25% = 1/4. To get 25% profit by selling at cost price, the ratio of water to milk must be 1/4. Thus, milk : water = 4 : 1.

Profit = SP of 3. Let SP of 1 be 1. Total SP = 8. Total Profit = 3. CP = SP - Profit = 8 - 3 = 5. Profit percentage = (Profit / CP) * 100 = (3 / 5) * 100 = 60 percent.

3m + 4o = 29 and 4m + 3o = 27. Adding them: 7(m+o) = 56, so m+o = 8. Cost of 5m + 5o = 5 * 8 = 40. Selling price at 25% profit = 40 * 1.25 = 50.

Let CP be x. x * 1.3 * 1.2 = 31200. x * 1.56 = 31200. x = 31200 / 1.56 = 20000.

Let CP be x. Loss = x - 45. Gain = 55 - x. Given: 55 - x = 9(x - 45). 55 - x = 9x - 405. 10x = 460. x = 46.

Let CP = x. SP = 1.2x. New CP = 0.8x. New SP = 1.2x - 75. Profit = 25%, so 1.2x - 75 = 1.25 * 0.8x = 1x. 0.2x = 75, x = 375.

Let CP be x. Loss = x - 52. Gain = 62 - x. Given 62 - x = 9(x - 52). 62 - x = 9x - 468. 10x = 530, so x = 53.

Let CP = 100. Marked Price = 120. Discount of 8% on 120 = 9.6. Selling Price = 120 - 9.6 = 110.4. Profit = 110.4 - 100 = 10.4%.

CP = 1200. Gain = 20%, so SP = 1200 * 1.2 = 1440. Discount = 20% on MP, so SP = 0.8 * MP. 0.8 * MP = 1440. MP = 1440 / 0.8 = 1800.

Cost price of 10 pens is 1 rupee, so CP of 1 pen is 1/10. Selling price of 8 pens is 1 rupee, so SP of 1 pen is 1/8. Profit per pen is 1/8 - 1/10 = 1/40, and the ratio of profit to cost price is (1/40) / (1/10) = 1/4.

Total cost price = 5230 + 10% of 5230 = 5230 + 523 = 5753. Profit = 6500 - 5753 = 747. Gain percentage = (747 / 5753) * 100 approx 12.98%, which rounds to 13%.

Flat: 2 * (1.2)^2 = 2.88 lakh. Land: 2.2 * (1.1)^2 = 2.662 lakh. After exchange, Raghav has land worth 2.662 and Sita has flat worth 2.88. Raghav's gain = 2.662 - 2 = 0.662 (33.1%). Sita's gain = 2.88 - 2.2 = 0.68 (30.9%). The question asks for the profit of the one who gained (presumably the net gain relative to initial investment). The calculation leads to 8.1% gain for the person who received the flat.