Profit, Loss and Discount

The total cost is Rs.840. One-fourth (Rs.210) is sold at 20% loss, so selling price = 210 - 20% of 210 = Rs.168. To gain 20% overall, total selling price should be 840 + 20% of 840 = Rs.1008. The remainder cost is Rs.630, so selling price needed = 1008 - 168 = Rs.840. Gain on remainder = (840 - 630)/630 = 33 1/3%.

Let the cost price be Rs. x. Selling at Rs. 800 causes a loss of (x - 800). Selling at Rs. 980 causes a gain of (980 - x), which is double the loss: 980 - x = 2(x - 800). Solving gives x = Rs. 875.

The gain is equal to the selling price of 30 mangoes when selling 150 mangoes. Gain percent = (Gain / Cost Price) × 100. Cost price of 150 mangoes = Selling price of 150 mangoes - Gain = Selling price of 150 mangoes - Selling price of 30 mangoes = Selling price of 120 mangoes. Therefore, gain percent = (30 / 120) × 100 = 25%.

Let the original price be Rs. x per kg. At original price, quantity bought = 385/x kg. After 20% reduction, price = 0.8x, quantity bought = 385/0.8x = 385/(0.8x) kg. The increase in quantity = 385/(0.8x) - 385/x = 3.5 kg. Solving gives x = Rs. 25 per kg.

Let the cost of the book sold at a loss be x. Then the other book costs 480 - x. Both are sold at the same price. The selling price of the first book is x - 15% of x = 0.85x. The selling price of the second book is (480 - x) + 19% of (480 - x) = 1.19(480 - x). Equating the selling prices: 0.85x = 1.19(480 - x). Solving gives x = Rs.140.

If the cost price (C.P) of 15 books equals the selling price (S.P) of 18 books, then the selling price of one book is (C.P of 15 books) / 18. The cost price of one book is (C.P of 15 books) / 15. Comparing these, the selling price per book is less than the cost price per book, indicating a loss. Calculating the loss percentage: Loss% = [(C.P - S.P) / C.P] × 100 = [(15/15 - 15/18) / (15/15)] × 100 = (1 - 5/6) × 100 = (1/6) × 100 = 16 2/3% loss. However, since the selling price per book is less than the cost price, the loss is 16 2/3%. The correct answer is A.

The cost price of one pen is Rs.9/8 = Rs.1.125. The selling price of one pen is Rs.8/9 ≈ Rs.0.8889. Since the selling price is less than the cost price, there is a loss. The loss percentage = ((1.125 - 0.8889)/1.125) × 100 ≈ 20.98%.

The selling price of each bicycle is Rs.990. For the first bicycle, with a 10% profit, cost price = 990 / 1.1 = Rs.900. For the second bicycle, with a 10% loss, cost price = 990 / 0.9 = Rs.1100. Total cost = 900 + 1100 = Rs.2000. However, this contradicts the options, so rechecking: 10% profit means SP = 110% of CP, so CP = SP / 1.1 = 900; 10% loss means SP = 90% of CP, so CP = SP / 0.9 = 1100; total cost = 900 + 1100 = Rs.2000. Option A is Rs.2000, so correct answer is A, not B. Correction made accordingly.

When selling two goats at the same price, one with a 10% profit and the other with a 10% loss, the overall effect is a loss. This is because the cost prices differ, and the combined transaction results in a net loss of approximately 1%.

The list price is Rs. 65. After the first discount of 10%, the price becomes 65 × 0.90 = Rs. 58.5. The customer pays Rs. 56.16 after the second discount. Let the second discount be x%. Then, 58.5 × (1 - x/100) = 56.16. Solving for x gives (1 - x/100) = 56.16 / 58.5 ≈ 0.96, so x ≈ 4%. Therefore, the other discount is 4%, which corresponds to option B.

Loss = Cost Price - Selling Price = 1500 - 1230 = 270. Loss % = (Loss / Cost Price) × 100 = (270 / 1500) × 100 = 18%. However, option A is 18%, so correct answer is A, not C. Rechecking calculation: 270/1500=0.18=18%. So correct answer is A.

Given that the cost price of 13 articles equals the selling price of 11 articles, the selling price of one article is (cost price of 13 articles) / 11 = (13/11) times the cost price of one article. The profit per article is therefore (13/11 - 1) = 2/11 of the cost price. The profit percentage is (2/11) × 100 = 18 2/11%. Hence, the correct answer is option B.

The trader marks the price 20% above cost price, so Marked Price = 1.2 × Cost Price. A 5% discount on the marked price means Selling Price = 0.95 × Marked Price = 0.95 × 1.2 × Cost Price = 1.14 × Cost Price. The gain is Rs.8400, so Gain = Selling Price - Cost Price = 0.14 × Cost Price = 8400. Therefore, Cost Price = 8400 / 0.14 = Rs.75000.

Given that the cost price (C.P) of 10 pens is equal to the selling price (S.P) of 12 pens, the selling price of one pen is less than its cost price, indicating a loss. Calculation: Let the cost price of one pen be C.P = x. Then, cost price of 10 pens = 10x. Selling price of 12 pens = 10x (given equal to cost price of 10 pens). So, selling price of one pen = (10x) / 12 = (5x) / 6. Loss per pen = C.P - S.P = x - (5x/6) = x/6. Loss percentage = (Loss / C.P) * 100 = (x/6) / x * 100 = 100/6 = 16 2/3 % loss. Therefore, the correct answer is option C: 16 2/3% loss.

Let the selling price be S and cost price be C. Selling at 2/3 S causes a 20% loss, so (2/3)S = 0.8C, which gives C = (2/3)S / 0.8 = (5/6)S. Profit percent when selling at S is ((S - C)/C)*100 = ((S - (5/6)S)/(5/6)S)*100 = (1/6)/(5/6)*100 = (1/5)*100 = 20%. However, this contradicts the options, so rechecking: Actually, C = (2/3)S / 0.8 = (2/3)S * (1/0.8) = (2/3)S * (5/4) = (5/6)S. Profit % = ((S - C)/C)*100 = ((S - (5/6)S)/(5/6)S)*100 = (1/6)/(5/6)*100 = (1/5)*100 = 20%. So profit percent is 20%, matching option A. But option A is 20%, so correct answer is A, not B. Therefore, correct answer is A.

Let the original cost price be Rs. x. The selling price with 20% profit is 1.2x. If bought at 20% less, cost price is 0.8x, and selling price is (1.2x - 75). Given this selling price yields 25% profit on 0.8x, so (1.2x - 75) = 1.25 * 0.8x = 1.0x. Solving 1.2x - 75 = x gives 0.2x = 75, so x = 375. However, this contradicts the calculation. Rechecking: 1.2x - 75 = 1.25 * 0.8x = 1.0x, so 1.2x - 75 = x, 0.2x = 75, x = 375. So original cost price is Rs.375, which matches option B. Therefore, correct answer is B. The initial explanation was missing; this explanation clarifies the solution.

Given that selling the house for Rs.45000 results in a gain of 1/8 of the cost price, the cost price (outlay) can be calculated as: Cost Price = Selling Price / (1 + Gain Fraction) = 45000 / (1 + 1/8) = 45000 / 1.125 = Rs.40000. To find the selling price for a 5% loss, multiply the cost price by 0.95: 40000 × 0.95 = Rs.38000. Therefore, the selling price to incur a 5% loss should be Rs.38000, which corresponds to option B.

Let the cost price be Rs. x. Selling at 10% loss means selling price = 0.9x. If sold for Rs.140 more, selling price = 0.9x + 140, which equals a 4% gain, so 1.04x = 0.9x + 140. Solving gives x = Rs. 3500. However, this conflicts with options, so re-check: 1.04x - 0.9x = 140 => 0.14x = 140 => x = 1000. So cost price is Rs.1000, which matches option A. Therefore, correct answer is A.

The total purchase amount is Rs. 25, which includes taxable and tax-free items. The sales tax paid is Rs. 0.30, and the tax rate is 6%. To find the taxable amount before tax, divide the tax paid by the tax rate: 0.30 / 0.06 = Rs. 5. This Rs. 5 is the cost of taxable items before tax. The total cost of taxable items including tax is Rs. 5 + Rs. 0.30 = Rs. 5.30. Therefore, the cost of tax-free items is the total purchase minus the total cost of taxable items including tax: 25 - 5.30 = Rs. 19.70. Hence, the correct answer is Rs. 19.70 (Option C).

First, calculate the rebate: 6% of Rs. 6650 = Rs. 399. So, the price after rebate = 6650 - 399 = Rs. 6251. Then, calculate sales tax: 10% of Rs. 6251 = Rs. 625.10. Total amount to pay = 6251 + 625.10 = Rs. 6876.10.

Let the original cost price be Rs. x. The selling price at 10% loss is 0.9x. If the cost price was 20% less, it would be 0.8x, and selling at Rs. 75 less means selling price is 0.9x - 75. This new selling price is 25% gain on 0.8x, so 0.9x - 75 = 1.25 * 0.8x = 1.0x. Solving 0.9x - 75 = x gives x = Rs. 250.

Let the original price be Rs. x per kg. After a 20% reduction, the price becomes 0.8x. With Rs. 120, the purchaser can buy 120/x kg originally and 120/(0.8x) kg after reduction. The difference is 3 kg: 120/(0.8x) - 120/x = 3. Solving gives x = Rs. 12.

To achieve a 25% profit on a cost price of Rs.47.50, the selling price must be Rs.47.50 × 1.25 = Rs.59.375. Since the article is sold after a 5% discount on the marked price, let the marked price be M. The selling price after discount is 95% of M, so 0.95 × M = 59.375. Solving for M gives M = 59.375 / 0.95 = Rs.62.50. Therefore, the article must be marked at Rs.62.50 to achieve the desired profit after the discount.

The man buys two articles for Rs.1980 each. On the first article, he gains 10%, so the selling price is 1980 + 10% of 1980 = Rs.2178. On the second article, he loses 10%, so the selling price is 1980 - 10% of 1980 = Rs.1782. The total cost price is 1980 + 1980 = Rs.3960. The total selling price is 2178 + 1782 = Rs.3960. Since the total selling price equals the total cost price, there is no overall gain or loss. Therefore, the total gain or loss percent is 0%, which corresponds to option D (no gain or no loss).

Let the cost price be Rs. x. Given that profit when selling at Rs. 832 equals loss when selling at Rs. 448, so profit = loss = (832 - x) = (x - 448). Solving gives x = Rs. 640. To make 50% profit, sale price = 1.5 × 640 = Rs. 960. However, the calculation shows 832 - 640 = 192 profit, and 640 - 448 = 192 loss, confirming cost price is Rs. 640. So 50% profit sale price = 640 + 0.5×640 = Rs. 960, which corresponds to option B. Therefore, the correct answer is B, not D.