Mathematics

The cost price (CP) of the article can be calculated using the selling price (SP) and profit percentage: CP = SP / (1 + profit%) = 800 / 1.25 = Rs.640. To make a loss of 25%, the selling price should be SP = CP × (1 - loss%) = 640 × 0.75 = Rs.480. Therefore, the shopkeeper should sell the article at Rs.480 to incur a 25% loss, which corresponds to option B.

The friend sells the car for Rs. 54,000 at a 20% gain, so the friend's cost price is Rs. 54,000 / 1.20 = Rs. 45,000. This Rs. 45,000 is the price at which the original man sold the car at a 10% loss, so the original cost price is Rs. 45,000 / 0.90 = Rs. 50,000. However, this calculation shows Rs. 50,000, which corresponds to option C, but the question asks for the original cost price of the car, which is Rs. 50,000. Therefore, the correct answer is C.

When the price of a toy is increased by 20%, the new price factor is 1.20. When the number of toys sold decreases by 15%, the new quantity factor is 0.85. The overall effect on sales revenue is the product of these two factors: 1.20 × 0.85 = 1.02, which means a 2% increase in sales revenue. Therefore, the sales revenue increases by 2%, corresponding to option C.

Let the cost price be Rs. x. The selling price at 10% loss is 0.9x. If bought for 20% less, cost price is 0.8x, and selling price is Rs. 0.9x + 55. Given profit is 40%, so selling price = 1.4 × 0.8x = 1.12x. Equate: 0.9x + 55 = 1.12x, solving gives x = Rs. 250.

The vendor bought 20 dozens at Rs. 15 each, total cost = 20 × 15 = Rs. 300. One-fourth were rotten, so remaining bananas = 20 × (3/4) = 15 dozens. He sold two-thirds of these (10 dozens) at Rs. 22.50 per dozen, earning Rs. 225. To break even, he must recover the remaining cost (300 - 225 = Rs. 75) by selling the remaining 5 dozens. So, price per dozen = 75 ÷ 5 = Rs. 15. However, since the question asks for the price per dozen to make neither profit nor loss, the correct price is Rs. 15 per dozen for the remaining bananas. But option B is Rs. 15, which matches this calculation. Therefore, the correct answer is B, not A. The original correct_answer was B, but option A is Rs. 20, which is incorrect. So the original correct_answer is correct. The explanation was missing and is now provided.

Given the ratio of sale price to cost price is 7:5, let the cost price be 5x and the sale price be 7x. Profit = Sale Price - Cost Price = 7x - 5x = 2x. The ratio of profit to cost price is therefore 2x : 5x = 2:5. Since the options given are A) 2:7, B) 5:2, C) 7:2, and D) Data inadequate, none of the first three options match the correct ratio 2:5. The correct answer should be 'Data inadequate' or an option indicating none of the above, but since 'Data inadequate' is the only remaining option, it is the best choice given the options. The original answer 'A' (2:7) is incorrect.

Let the cost of a horse be x and the cost of a cow be y. Then, 4x + 9y = 13,400. The total profit is Rs. 1880, which comes from 10% profit on horses and 20% profit on cows: 0.10(4x) + 0.20(9y) = 1880. Solving these equations gives x = Rs. 2500, so the cost of a horse is Rs. 2500.

Let the total stock be Rs. x. Selling 20% at 10% profit gives profit = 0.2x * 10% = 0.02x. Selling 80% at 5% loss gives loss = 0.8x * 5% = 0.04x. Overall loss = 0.04x - 0.02x = 0.02x = Rs. 400, so x = 400 / 0.02 = Rs. 20,000.

Kabir sells the article for Rs. 660 at a 10% profit, so the cost price is Rs. 660 ÷ 1.10 = Rs. 600. Since he bought it at a 25% discount, the cost price is 75% of the marked price. Therefore, marked price = Rs. 600 ÷ 0.75 = Rs. 800.

Let the cost price be C and the original selling price be S. The original profit is S - C. When the selling price is doubled, it becomes 2S, and the new profit is 2S - C. Given that the new profit triples the original profit, we have 2S - C = 3(S - C). Simplifying: 2S - C = 3S - 3C => 2C = S. So, the original selling price is twice the cost price. The original profit is S - C = C, which means the profit is equal to the cost price. Therefore, the profit percentage is (Profit / Cost Price) × 100 = (C / C) × 100 = 100%. Hence, the correct profit percent is 100%, which corresponds to option B.

Raheem's total cost price is the sum of the purchase price and repair costs: Rs. 42,000 + Rs. 13,000 = Rs. 55,000. He sold the car for Rs. 64,900, so his profit is Rs. 64,900 - Rs. 55,000 = Rs. 9,900. The profit percentage is calculated as (Profit / Cost Price) × 100 = (9,900 / 55,000) × 100 = 18%. Therefore, the correct profit percentage is 18%, which corresponds to option C.

Given that the cost price (CP) of 50 articles equals the selling price (SP) of 40 articles, the SP per article is higher than the CP per article, indicating a profit. Calculating the profit percentage: Let the cost price of one article be 1 unit. Then, CP of 50 articles = 50 units, and SP of 40 articles = 50 units. So, SP of one article = 50/40 = 1.25 units. Profit per article = SP - CP = 1.25 - 1 = 0.25 units. Profit percentage = (Profit / CP) × 100 = (0.25 / 1) × 100 = 25%. Since 25% profit is not listed among the options, the closest available option is 20% profit (option B).

If the plot is sold at Rs. 18,700 with a 15% loss, the cost price (CP) is Rs. 18,700 ÷ 0.85 = Rs. 22,000. To gain 15%, the selling price (SP) should be CP × 1.15 = Rs. 22,000 × 1.15 = Rs. 25,300. However, since Rs. 25,300 is option C, but the calculation shows it should be the correct answer, the original correct_answer was C. Rechecking: 22,000 × 1.15 = 25,300, so option C is correct. Therefore, the original correct_answer C is correct. The explanation is added and difficulty set to medium as it involves percentage calculations.

The greatest possible profit per book is when the book is bought at the lowest price (Rs. 200) and sold at the highest price (Rs. 425), giving a profit of Rs. 225 per book. For 8 books, the greatest possible profit is 8 × Rs. 225 = Rs. 1800. Since Rs. 1800 is not among the given options, the correct choice is 'None of these' (Option D). The previously given answer (Rs. 600) is incorrect because it does not represent the maximum possible profit based on the given price ranges.

Let the cost price be Rs. x. The percentage profit equals the percentage loss, so (1920 - x)/x = (x - 1280)/x. Solving gives x = Rs.1600. To make 25% profit, selling price = 1600 + 25% of 1600 = Rs. 2000. However, option A is Rs. 2000, which matches this calculation, so the correct answer is A, not C. Rechecking the calculation: (1920 - x)/x = (x - 1280)/x implies 1920 - x = x - 1280, so 2x = 3200, x = 1600. Selling price for 25% profit = 1600 * 1.25 = Rs. 2000. Therefore, correct answer is A.

Let the marked price be 100 units. The shopkeeper offers a 5% discount, so the selling price is 95 units. Given a profit of 23.5%, the cost price (CP) can be calculated as CP = Selling Price / (1 + Profit%) = 95 / 1.235 ≈ 76.9 units. If no discount was offered, the selling price would be the full marked price of 100 units. The profit percentage without discount would then be ((100 - 76.9) / 76.9) × 100 ≈ 30%. Therefore, the correct answer is 30%, option C.

Let the labelled price be Rs. x. With 20% discount, Tarun pays 0.8x. With 25% discount, he would pay 0.75x. The difference in price is 0.8x - 0.75x = 0.05x, which equals Rs. 500. So, 0.05x = 500, giving x = 10000. The price Tarun paid is 80% of 10000 = Rs. 8000, but this is not an option. The question asks for the price he bought the TV, so the labelled price is Rs. 10000, and the price he paid is Rs. 8000. Since Rs. 8000 is not an option, the closest correct labelled price is Rs. 10000 (option B). However, the question asks for the price he bought the TV, so the correct answer should be Rs. 8000, which is missing. Among the options, Rs. 16000 (option D) is incorrect. Therefore, the question and options are inconsistent. Given this, the labelled price is Rs. 10000, and the price he paid is Rs. 8000. Since Rs. 8000 is not an option, the best answer is Rs. 10000 (option B) as the labelled price. The question should be rephrased or options corrected.

The cost price (CP) is Rs. 250 (since selling at Rs. 300 gives 20% gain). The marked price (MP) is Rs. 300. During the sale, a 10% discount on MP means selling price (SP) = 300 - 10% of 300 = Rs. 270. Gain = SP - CP = 270 - 250 = Rs. 20. Gain percent = (20/250)*100 = 8%. However, the options given are 7, 7.5, 8, and 9, and the correct gain percent is 8%. So the correct answer should be C, not B. Rechecking calculations: CP = SP / (1 + gain%) = 300 / 1.2 = 250; SP during sale = 300 * 0.9 = 270; Gain = 270 - 250 = 20; Gain% = (20/250)*100 = 8%. Therefore, the original correct answer C is correct. The explanation was missing and has been added. Difficulty is medium due to percentage calculations and discount concepts. Tags added accordingly.

Given the ratio of cost price (CP) to selling price (SP) is 4:5, the profit is SP - CP = 5x - 4x = x. Profit percent = (Profit/CP) * 100 = (x/4x)*100 = 25%.

The shopkeeper buys two articles for Rs. 1000 each, so total cost price = Rs. 2000. He sells the first article at 20% profit, so selling price of first article = 1000 + 20% of 1000 = Rs. 1200. He sells the second article at 20% loss, so selling price of second article = 1000 - 20% of 1000 = Rs. 800. Total selling price = 1200 + 800 = Rs. 2000, which is equal to the total cost price. Therefore, there is no net profit or loss, and the net profit or loss percent is 0%. Hence, the correct answer is 'neither profit nor loss' (Option A).

The dealer marks goods 20% above cost price, so marked price = 120% of cost. He makes an 8% profit after discount, so selling price = 108% of cost. The discount is the difference between marked price and selling price, which is 120% - 108% = 12%. Hence, the discount rate is 12%.

Given that the selling price of 50 articles equals the cost price of 40 articles, the selling price per article is (cost price of 40 articles) / 50 = (40/50) times the cost price per article = 0.8 times the cost price. This means the selling price is 80% of the cost price, resulting in a loss. The loss percentage is calculated as ((cost price - selling price) / cost price) × 100 = ((1 - 0.8) × 100) = 20%. Therefore, there is a 20% loss, which corresponds to option A.

A 25% rebate on a shirt costing Rs. 32 means a rebate of Rs. 8 per shirt (25% of 32). To get a total rebate of Rs. 40, one must buy 40 ÷ 8 = 5 shirts. However, the options and calculation show 5 as option B, but the correct answer is 5, so the original correct_answer was B, which is correct. Rechecking: 25% of 32 = 8; 40 ÷ 8 = 5. So the correct answer is B, not C. The initial correction was wrong. The original correct_answer B is correct.

The cost price (CP) of 70 kg of potatoes is Rs. 420, so the cost price per kg is Rs. 420 ÷ 70 = Rs. 6. The selling price (SP) per kg is Rs. 6.50. The total selling price is 70 × 6.50 = Rs. 455. The gain is SP - CP = Rs. 455 - Rs. 420 = Rs. 35. The gain percent is (Gain / CP) × 100 = (35 / 420) × 100 = 8.33%, which is 8 1/3%. Therefore, the correct answer is option C.

The cost price (CP) is 64% of the marked price (MP), so CP = 0.64 MP. A discount of 12% on MP means selling price (SP) = 0.88 MP. Gain = SP - CP = 0.88 MP - 0.64 MP = 0.24 MP. Gain percent = (Gain/CP) × 100 = (0.24 MP / 0.64 MP) × 100 = 37.5%.