Mathematics

The man sold 20 articles for Rs. 60 and gained 20%. This means the selling price (SP) of 20 articles is Rs. 60, and the gain is 20%. To find the cost price (CP) of 20 articles, use the formula SP = 1.2 × CP (since gain is 20%). Thus, CP = 60 / 1.2 = Rs. 50 for 20 articles. The cost price per article is Rs. 50 / 20 = Rs. 2.5. With Rs. 60, the number of articles he can buy is 60 / 2.5 = 24 articles. Therefore, the correct answer is option B (24 articles).

Samad bought 20 dozens (240 toys) at Rs. 375 per dozen, so total cost = 20 × 375 = Rs. 7500. He sold each toy at Rs. 33, so total revenue = 240 × 33 = Rs. 7920. Profit = 7920 - 7500 = Rs. 420. Percentage profit = (420 / 7500) × 100 = 5.6%. However, the calculation shows 5.6%, which matches option C, but rechecking the math: 20 dozens = 240 toys; cost price per toy = 375/12 = 31.25; total cost = 31.25 × 240 = 7500; selling price per toy = 33; profit per toy = 1.75; total profit = 1.75 × 240 = 420; percentage profit = (420/7500)×100 = 5.6%. So the correct answer is C, not D. The initial explanation was incorrect. Therefore, correct answer is C.

The sale price including sales tax is Rs. 616, and the sales tax rate is 10%, so the price before tax is Rs. 616 ÷ 1.10 = Rs. 560. The shopkeeper made a 12% profit, so the cost price is Rs. 560 ÷ 1.12 = Rs. 500.

The equivalent single discount for successive discounts of 10%, 20%, and 40% is calculated as 1 - (0.9 × 0.8 × 0.6) = 1 - 0.432 = 0.568 or 56.8%.

Given that selling 20 toffees for 1 rupee results in a 40% loss, the cost price (CP) for 20 toffees is higher than 1 rupee. Specifically, CP = Selling Price / (1 - Loss%) = 1 / (1 - 0.40) = 1 / 0.60 = 1.6667 rupees for 20 toffees. To gain 20%, the selling price must be 1.2 times the cost price, so new selling price = 1.2 × 1.6667 = 2 rupees for 20 toffees. Therefore, for 1 rupee, the number of toffees to sell = (20 toffees) × (2 rupees / 1 rupee) = 40 toffees / 2 = 16 toffees. Hence, to gain 20%, he must sell 16 toffees for 1 rupee.

Let the marked price be M. The retailer gets a 15% discount, so he buys the machine at 85% of M, i.e., 0.85M. He sells it for Rs. 1955 and makes a 15% profit on his cost price (0.85M). Therefore, selling price = cost price × 1.15 = 0.85M × 1.15 = 0.9775M. Given selling price = Rs. 1955, so 0.9775M = 1955 ⇒ M = 1955 / 0.9775 ≈ Rs. 2000. The discount is 15% of M = 0.15 × 2000 = Rs. 300. Hence, the discount amount is Rs. 300, which corresponds to option C.

The problem involves calculating the marked price based on the difference in profit when the discount changes from 5% to 7%. By setting up equations for profit at both discount rates and using the Rs. 15 difference, the marked price is found to be Rs. 712.50.

The shopkeeper buys 4 mangoes for 1 rupee, so the cost price per mango is 1/4 rupee. He sells 3 mangoes for 1 rupee, so the selling price per mango is 1/3 rupee. The cost price for 3 mangoes is 3 × (1/4) = 3/4 rupee, and the selling price for 3 mangoes is 1 rupee. Profit = 1 - 3/4 = 1/4 rupee. Profit percent = (Profit / Cost Price) × 100 = (1/4) / (3/4) × 100 = 33 1/3%.

Let the original cost price be Rs. x. Repairs cost = 10% of x = 0.1x. Total cost price = x + 0.1x = 1.1x. Profit = Rs. 1100 and profit percentage = 20%. Profit percentage is calculated on total cost price, so 20% of total cost price = Rs. 1100. Therefore, 0.20 × 1.1x = 1100, which gives 0.22x = 1100, so x = 1100 / 0.22 = 5000. Repairs cost = 10% of 5000 = Rs. 500. Hence, the correct answer is Rs. 500, which corresponds to option C.

If selling at Rs. 102 results in a 15% loss, the cost price (CP) can be calculated as Rs. 102 ÷ 0.85 = Rs. 120. To gain 20%, the selling price should be CP + 20% of CP = Rs. 120 × 1.20 = Rs. 144. Therefore, the correct selling price to gain 20% is Rs. 144, which corresponds to option B.

Let the marked price be Rs. M. The discount is 20% of M = 0.2M. The selling price is M - 0.2M = 0.8M. Given a gain of 20%, cost price = selling price / 1.2 = 0.8M / 1.2 = (2/3)M. Profit = selling price - cost price = 0.8M - (2/3)M = (0.8 - 0.6667)M = 0.1333M. Profit is Rs. 6 less than discount, so discount - profit = 6 => 0.2M - 0.1333M = 6 => 0.0667M = 6 => M = 90. Selling price = 0.8 * 90 = Rs. 72.

The labelled price (LP) can be calculated from the discounted price: Rs. 12,500 = 80% of LP, so LP = 12,500 / 0.8 = Rs. 15,625. The total cost price including transport and installation is Rs. 12,500 + 125 + 250 = Rs. 12,875. To earn a 10% profit on the labelled price without discount, the selling price should be 110% of LP = 1.1 × 15,625 = Rs. 17,187.5. Since no discount is offered on selling, the selling price must be at least Rs. 17,187.5. The closest option given is Rs. 17,600, which ensures the desired profit margin. Therefore, option D is correct.

A's share of the capital is 1/3. The total profit is Rs.2460, so A's share of the profit = (1/3) × 2460 = Rs.820. However, the sum of the given fractions 1/3 + 1/4 + 1/5 = 47/60, so D's share is 13/60. Calculating A's share of profit correctly: A's fraction is 1/3 = 20/60, so A's profit share = (20/60) × 2460 = Rs.820. Therefore, option C (Rs.820) is correct, not B.

The total cost of the mixture is calculated as (80 kg × Rs. 6.75) + (120 kg × Rs. 8) = Rs. 540 + Rs. 960 = Rs. 1500. The total weight of the mixture is 80 kg + 120 kg = 200 kg. Therefore, the cost price per kg of the mixture is Rs. 1500 ÷ 200 = Rs. 7.50. To gain 20%, the selling price per kg must be 7.50 × 1.20 = Rs. 9.00. Hence, the correct selling price to gain 20% is Rs. 9.00 per kg, which corresponds to option D.

The dealer uses 900 g instead of 1000 g but charges for 1000 g, so gain = (1000 - 900)/900 × 100% = 100/900 × 100% = 11 1/9%.

The shopkeeper sells 400 metres for Rs. 18000 at a loss of Rs. 5 per metre. The selling price per metre is 18000/400 = Rs. 45. Since there is a loss of Rs. 5 per metre, the cost price per metre = selling price + loss = 45 + 5 = Rs. 50. However, option D is Rs. 50, which matches this calculation, so the correct answer is D, not A. Therefore, the original correct_answer 'D' is correct. The explanation clarifies the calculation.

When a man sells two items at the same price, gaining 5% on one and losing 5% on the other, the overall effect is a loss. The net loss percentage is calculated as (gain% × loss%) / 100 = (5 × 5)/100 = 0.25% loss.

Given that the selling price (SP) is Rs.600 and the profit is 25%, the cost price (CP) can be calculated using the formula: CP = SP / (1 + Profit%) = 600 / 1.25 = Rs.480. Therefore, the correct cost price is Rs.480, which corresponds to option D.

The man sells 320 mangoes at the cost price of 400 mangoes. This means the selling price (SP) is equal to the cost price (CP) of 400 mangoes, while the cost price is for 320 mangoes. The gain is the difference between SP and CP, which is the cost price of 80 mangoes (400 - 320). The gain percent is calculated as (Gain / CP) × 100 = (80 / 320) × 100 = 25%. Therefore, the gain percent is 25%, corresponding to option D.

The trader lists the articles at 20% above cost price, so the marked price is 120% of C.P. After allowing a 10% discount, the selling price becomes 90% of the marked price, i.e., 0.9 × 120% = 108% of C.P. Thus, the gain percent is 8%.

The refrigerator was sold at a 4% loss on Rs. 15000, which is a loss of Rs. 600. The mobile phone was sold at a 10% profit on Rs. 8000, which is a profit of Rs. 800. Overall, the net gain is Rs. 800 - Rs. 600 = Rs. 200 profit. However, the question asks for overall result, so the correct calculation is: Loss on refrigerator = 4% of 15000 = 600; Profit on mobile = 10% of 8000 = 800; Net = 800 - 600 = Rs. 200 profit. The correct answer should be profit of Rs. 200, which corresponds to option D. But since the original options include an extra option E (None of these), and the original correct answer is D, the options need to be corrected to only four options as per instructions, removing option E. After removing option E, the correct answer remains D. Therefore, the original correct answer D is correct but option E is invalid and should be removed. The question text has minor grammar issues fixed.

Let the cost price be Rs. x. The profit percent is equal to the cost price, so profit = x% of x = (x*x)/100. The selling price is cost price plus profit: x + (x^2)/100 = 75. Multiplying both sides by 100: 100x + x^2 = 7500, or x^2 + 100x - 7500 = 0. Solving this quadratic gives x = 50 (positive root). Hence, the cost price is Rs. 50.

The rate of discount is calculated as (Discount / Marked Price) × 100 = ((80 - 68) / 80) × 100 = (12 / 80) × 100 = 15%. However, the option C '17 11/17%' is incorrect. The correct discount rate is 15%, which corresponds to option A. Therefore, the original correct_answer 'A' is correct, but option C is incorrect. Since the question asks for the rate of discount, the correct answer is 15%.

If the cost price of 12 pens equals the selling price of 8 pens, then the selling price of 1 pen is (cost price of 12 pens) / 8 = 1.5 times the cost price of 1 pen. This means a 50% gain on the cost price. However, gain percent is calculated as (Gain / Cost Price) × 100 = ((SP - CP)/CP) × 100. Here, SP = 1.5 CP, so gain = 0.5 CP, gain percent = (0.5/1) × 100 = 50%. But the options suggest a different interpretation: The gain percent is ((SP - CP)/CP) × 100 = ((12/8 - 1) × 100) = (1.5 - 1) × 100 = 50%. The correct answer is 50%, which corresponds to option C. However, the original answer was C but the explanation was missing. The explanation is now provided.

The cost price of the first article is Rs. 1000 / 1.2 = Rs. 833.33, and the cost price of the second article is Rs. 1000 / 0.8 = Rs. 1250. Total cost price = Rs. 833.33 + Rs. 1250 = Rs. 2083.33. Total selling price = Rs. 2000. Since selling price < cost price, there is a net loss. Net loss = Rs. 2083.33 - Rs. 2000 = Rs. 83.33, which is approximately 4% loss on total cost price.