Mathematics

If the man gains 20% by selling at price P, then the cost price (C) is P/1.2. Selling at double the price (2P) results in profit = 2P - C = 2P - P/1.2 = 2P - 0.8333P = 1.1667P. The profit percentage = (Profit / Cost Price) × 100 = (1.1667P / (P/1.2)) × 100 = 1.1667 × 1.2 × 100 = 140%. Therefore, the profit percentage when selling at double the original price is 140%.

If selling at Rs. 5.40 per kg results in a 10% loss, the cost price (CP) is Rs. 6.00 (since 5.40 = 90% of CP). To earn a 20% profit, the selling price should be 120% of CP, which is Rs. 7.20. However, option D is Rs. 7.20, but the calculation shows Rs. 7.20, so option D is correct. Rechecking: CP = 5.40 / 0.9 = 6.00; required SP = 6.00 * 1.20 = 7.20. So option D is correct. The initial correct_answer was D, which matches the calculation. Explanation was missing and has been added. Difficulty set to medium as it involves percentage profit and loss calculations.

Given that selling 12 oranges for one rupee results in a 20% loss, the cost price (CP) of 12 oranges can be calculated as follows: Since selling price (SP) is 1 rupee for 12 oranges and this is 80% of CP (because of 20% loss), CP = 1 / 0.8 = 1.25 rupees for 12 oranges. To gain 20%, the selling price should be 120% of CP, i.e., SP = 1.25 × 1.2 = 1.5 rupees for 12 oranges. Now, to find how many oranges should be sold for 1 rupee to gain 20%, we calculate the number of oranges per rupee as (12 oranges) / (1.5 rupees) = 8 oranges per rupee. Therefore, the man should sell 8 oranges for one rupee to gain 20%. The original answer (15 oranges) and explanation were incorrect and inconsistent with the calculations.

Let the cost price be Rs. x. Profit when selling at Rs. 425 is (425 - x), and loss when selling at Rs. 355 is (x - 355). Given they are equal, 425 - x = x - 355, solving gives x = Rs. 390. However, checking options, Rs. 390 is option B, so the correct answer is B, not A. Rechecking: 425 - 390 = 35 profit, 390 - 355 = 35 loss, equal indeed. So correct answer is B.

The trader marks the price 30% above cost price, so Marked Price = 1.3 × Cost Price. A 10% discount on the marked price means the selling price = 0.9 × Marked Price = 0.9 × 1.3 × Cost Price = 1.17 × Cost Price. Given gain = Rs.340, so Selling Price - Cost Price = 340, which gives 1.17 × Cost Price - Cost Price = 340, or 0.17 × Cost Price = 340. Solving, Cost Price = 340 / 0.17 = Rs.2000.

Given the ratio 4:5:7, let the common multiplier be x. The difference between the costliest and cheapest cars is 7x - 4x = 3x = 60000, so x = 20000. The modest price corresponds to 5x = 5 * 20000 = Rs. 100000.

The total cost price is Rs. 16000 + Rs. 6250 = Rs. 22250. The selling price is Rs. 31150. Profit = 31150 - 22250 = Rs. 8900. Profit percentage = (8900 / 22250) × 100 ≈ 40%. Hence, option C is correct.

Let the printed price be P and the cost price be C. The selling price (SP) is 10% discount on printed price, so SP = 0.9 × P. The shopkeeper earns 12% profit on cost price, so SP = 1.12 × C. Equating, 1.12 × C = 0.9 × P, which gives C/P = 0.9/1.12 = 45/56. Therefore, the ratio of cost price to printed price is 45:56, which corresponds to option A.

The horse sold at a 20% loss means its cost price was Rs. 15000 (since 80% of 15000 = 12000). The cow sold at a 20% gain means its cost price was Rs. 10000 (since 120% of 10000 = 12000). Total cost price = 15000 + 10000 = 25000; total selling price = 12000 + 12000 = 24000. Hence, there is a loss of Rs. 1000 in the entire transaction.

Ramees bought 4 dozen apples at Rs. 12 per dozen (cost = 4 × 12 = Rs. 48) and 2 dozen apples at Rs. 16 per dozen (cost = 2 × 16 = Rs. 32). Total cost = Rs. 80 for 6 dozen apples. To earn 20%, selling price = 80 × 1.2 = Rs. 96. Price per dozen = 96 ÷ 6 = Rs. 16.80.