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Question 1 / 20
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1
A seller has 200 units of an item. Some units are sold at a 10% profit, and the rest at a 25% profit, resulting in an overall 15% profit. How many units were sold at a 25% profit?
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Solution: Step 1: Assume cost price per unit = Rs. 1 Total cost price = 200 units * Rs. 1 = Rs. 200 Step 2: Let x units be sold at 25% profit. Then, (200 - x) units are sold at 10% profit. Step 3: Set up equation for total profit. 1.25x + 1.10(200 - x) = 1.15 * 200 Step 4: Simplify equation. 1.25x + 220 - 1.10x = 230 0.15x = 10 x = 10 / 0.15 ≈ 66.67 Step 5: Nearest option to 66.67 is 67 units
2
An article was sold for Rs. 950 after a 5% discount was applied to its marked price. What was the marked price of the article?
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Solution: Step 1: Let the Marked Price (MP) be 'x'. Step 2: The discount allowed is 5% of the MP. Step 3: The Selling Price (SP) is MP - Discount = x - 0.05x = 0.95x. Step 4: We are given that SP = Rs. 950. Step 5: Set up the equation: 0.95x = 950. Step 6: Solve for x: x = 950 / 0.95. Step 7: x = 1000. Step 8: The marked price of the article was Rs. 1000.
3
A trader earns a 20% profit on one transaction and incurs a 20% loss on another when selling two items for Rs. 4000 each. What is the overall profit or loss percentage for both transactions?
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Solution: Step 1: Let CP for first item = x, then SP = 1.2x (20% profit) Step 2: Let CP for second item = y, then SP = 0.8y (20% loss) Step 3: Given SP for both items = Rs. 4000 each Step 4: 1.2x = 4000 => x = 4000 / 1.2 ≈ 3333.33 Step 5: 0.8y = 4000 => y = 4000 / 0.8 = 5000 Step 6: Total CP = x + y = 3333.33 + 5000 = Rs. 8333.33 Step 7: Total SP = 4000 + 4000 = Rs. 8000 Step 8: Loss = Total CP - Total SP = 8333.33 - 8000 = Rs. 333.33 Step 9: Loss percentage = (333.33 / 8333.33) * 100 ≈ 4% Answer: Loss = 4%
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A seller incurs a 10% loss on an item. If the selling price had been increased by Rs. 125, a 15% profit would have been made. What is the cost price of the item in Rs.?
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Solution: Step 1: Let the cost price = x Rs. Step 2: Selling price at 10% loss = 0.9x Rs. Step 3: Selling price at 15% profit = 1.15x Rs. Step 4: According to the question: 0.9x + 125 = 1.15x Step 5: Rearrange equation: 125 = 1.15x - 0.9x Step 6: Simplify: 125 = 0.25x Step 7: Solve for x: x = 125 / 0.25 = 500 Rs. Step 8: Cost price = 500 Rs.
5
A fruit seller purchases oranges. By selling 40% of them, he recovers the total cost price of all the oranges. Later, he sells 80% of the remaining oranges at half the initial profit rate per orange. The last remaining oranges are rotten and discarded. What is his overall profit percentage?
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Solution: Step 1: Assume the fruit seller buys 100 oranges for a total Cost Price (CP) of Rs. 100. Thus, CP per orange is Rs. 1. Step 2: **First Sale (40% of oranges):** - He sells 40% of 100 oranges = 40 oranges. - He recovers the total cost price of all oranges (Rs. 100) from this sale. So, Selling Price (SP) of 40 oranges = Rs. 100. - The CP of these 40 oranges = 40 * Rs. 1 = Rs. 40. - Profit on these 40 oranges = SP - CP = 100 - 40 = Rs. 60. - Profit rate for the first sale: Profit % = (60 / 40) * 100 = 150%. Step 3: **Second Sale (80% of remaining oranges):** - Remaining oranges = 100 - 40 = 60 oranges. - He sells 80% of these 60 remaining oranges = 0.80 * 60 = 48 oranges. - These 48 oranges are sold at half the previous profit rate, so 150% / 2 = 75% profit. - The CP of these 48 oranges = 48 * Rs. 1 = Rs. 48. - SP of these 48 oranges = CP + (75% of CP) = 48 + (0.75 * 48) = 48 + 36 = Rs. 84. Step 4: **Rotten Oranges:** - Remaining after the second sale = 60 - 48 = 12 oranges. - These 12 oranges are rotten and discarded, generating no revenue. Step 5: **Calculate Overall Profit:** - Total CP = Rs. 100. - Total SP = SP from first sale + SP from second sale = 100 + 84 = Rs. 184. - Overall Profit = Total SP - Total CP = 184 - 100 = Rs. 84. Step 6: **Calculate Overall Profit Percentage:** - Overall Profit % = (Overall Profit / Total CP) * 100 = (84 / 100) * 100 = 84%.
6
Person A purchased an item for Rs.80,000 and sold it to Person B at a 20% profit. Person B then spent Rs.4,000 on maintenance and sold it to Person C at an 18% loss. Determine the price at which Person C purchased the item.
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Solution: Step 1: Calculate selling price from Person A to Person B = 80,000 * 1.20 = Rs.96,000 Step 2: Person B's total cost after maintenance = 96,000 + 4,000 = Rs.100,000 Step 3: Calculate selling price from Person B to Person C = 100,000 * 0.82 = Rs.82,000 Step 4: Final price Person C paid = Rs.82,000
7
A vendor makes an 18% profit selling items at a certain price. By increasing the price by ₹1, the profit increases to 38%. Find the new selling price.
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Solution: Step 1: Let cost price = x ₹ Step 2: Selling price at 18% profit = 1.18x ₹ Step 3: Selling price at 38% profit = 1.38x ₹ Step 4: According to the question: 1.18x + 1 = 1.38x Step 5: Rearrange equation: 1 = 1.38x - 1.18x Step 6: Simplify: 1 = 0.2x Step 7: Solve for x: x = 1 / 0.2 = 5 ₹ Step 8: New selling price = 1.38 * 5 = ₹6.9
8
An individual purchases a bicycle for Rs. 1400 and sells it at a 15% loss. Determine the selling price of the bicycle.
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Solution: Step 1: Calculate the loss amount: 15% of Rs. 1400 = 0.15 * 1400 = Rs. 210 Step 2: Calculate the selling price: Selling Price = Cost Price - Loss = Rs. 1400 - Rs. 210 = Rs. 1190
9
Sanjay sold a shirt with an 8% profit after offering a 12% discount on its marked price. If the shirt's marked price is Rs. 1080, what is its cost price?
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Solution: Step 1: Given Marked Price (MP) = Rs. 1080. Step 2: Calculate the discount amount. Discount = 12% of MP = 0.12 × 1080 = Rs. 129.60. Step 3: Calculate the Selling Price (SP) after the discount. SP = MP - Discount = 1080 - 129.60 = Rs. 950.40. Step 4: Sanjay made an 8% profit on this Selling Price. Let the Cost Price (CP) be 'x'. SP = CP × (100 + Profit%)/100. Step 5: Substitute known values: 950.40 = x × (108/100). Step 6: Solve for x: x = (950.40 × 100) / 108 = 95040 / 108. Step 7: x = 880. Step 8: The Cost Price of the shirt is Rs. 880.
10
A shopkeeper sells one transistor for Rs. 840, making a 20% gain, and another for Rs. 960, incurring a 4% loss. What is his total gain or loss percentage?
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Solution: Step 1: Calculate the Cost Price (CP) of the first transistor. Step 2: For the first transistor, SP1 = Rs. 840 and Gain% = 20%. So, CP1 = SP1 * 100 / (100 + Gain%) = 840 * 100 / 120 = Rs. 700. Step 3: Calculate the Cost Price (CP) of the second transistor. Step 4: For the second transistor, SP2 = Rs. 960 and Loss% = 4%. So, CP2 = SP2 * 100 / (100 - Loss%) = 960 * 100 / 96 = Rs. 1000. Step 5: Calculate the Total Cost Price (Total CP) = CP1 + CP2 = 700 + 1000 = Rs. 1700. Step 6: Calculate the Total Selling Price (Total SP) = SP1 + SP2 = 840 + 960 = Rs. 1800. Step 7: Since Total SP (Rs. 1800) > Total CP (Rs. 1700), there is a total gain. Step 8: Total Gain = Total SP - Total CP = 1800 - 1700 = Rs. 100. Step 9: Calculate Total Gain Percentage = (Total Gain / Total CP) * 100. Step 10: Total Gain% = (100 / 1700) * 100 = 100 / 17 %. Step 11: 100/17% is equivalent to 5 15/17% gain.
11
A retailer sells two items for a total of 5000 units. The cost price of the first item equals the selling price of the second. The first item is sold at a 33.33% loss, while the second is sold at a 60% gain. Determine the overall profit or loss.
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Solution: Step 1: Let S.P of first item = x units Step 2: S.P of second item = 5000 - x units Step 3: C.P of first item = S.P of second item = 5000 - x units Step 4: Loss on first item = 33.33% of (5000 - x) = (1/3)(5000 - x) Step 5: Set up equation: x = (5000 - x) - (1/3)(5000 - x) Step 6: Simplify: x = (2/3)(5000 - x) Step 7: Solve for x: 3x = 2(5000 - x) => 5x = 10000 => x = 2000 Step 8: S.P of second item = 5000 - 2000 = 3000 units Step 9: Profit on second item = 60% => C.P of second item = (3000 * 100) / 160 = 1875 units Step 10: Total C.P = (5000 - 2000) + 1875 = 4875 units Step 11: Overall Profit = 5000 - 4875 = 125 units
12
An article with a marked price of Rs. 720 receives two successive discounts, each of x%. If the total discount amounts to Rs. 259.20, what is the value of x?
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Solution: Step 1: Identify the Marked Price (MP) = Rs. 720. Step 2: Identify the Total Discount amount = Rs. 259.20. Step 3: Calculate the equivalent single discount percentage = (Total Discount Amount / MP) * 100. Step 4: Equivalent Discount % = (259.20 / 720) * 100 = 36%. Step 5: For two successive discounts of x%, the equivalent single discount percentage (D_eq) is given by D_eq = x + x - (x * x / 100). Step 6: Set up the equation: 36 = 2x - (x^2 / 100). Step 7: Multiply by 100: 3600 = 200x - x^2. Step 8: Rearrange into a quadratic equation: x^2 - 200x + 3600 = 0. Step 9: Test the given options. For x = 20: Equivalent discount = 20 + 20 - (20 * 20 / 100) = 40 - 4 = 36%. Step 10: Since this matches the calculated equivalent discount, x = 20.
13
A retailer purchases a grinder with a 15% discount from a wholesaler and then sells it for Rs. 1955, making a 15% profit. What was the amount of discount the retailer received from the wholesaler?
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Solution: Step 1: Given the selling price (SP) of the grinder for the retailer = Rs. 1955. Step 2: The retailer made a profit of 15%. To find the cost price (CP) for the retailer: CP = SP / (1 + Profit%/100). Step 3: CP = 1955 / (1 + 15/100) = 1955 / 1.15 = Rs. 1700. Step 4: The retailer purchased the grinder at a 15% discount from the wholesaler. This means Rs. 1700 is 85% of the wholesaler's marked price (MP). Step 5: Let the wholesaler's marked price be Y. So, 0.85Y = 1700. Step 6: Solve for Y: Y = 1700 / 0.85 = Rs. 2000. Step 7: The amount of discount received by the retailer from the wholesaler is the difference between the wholesaler's marked price and the retailer's cost price. Step 8: Discount amount = MP - CP = 2000 - 1700 = Rs. 300. Step 9: Alternatively, discount amount = 15% of MP = 0.15 * 2000 = Rs. 300.
14
An article is sold for Rs. 75, and the profit percentage earned is numerically equal to its cost price in rupees. What is the cost price of the article?
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Solution: Step 1: Let the Cost Price (CP) be Rs. 'x'. Step 2: Given that the Profit Percentage is numerically equal to the CP, so Profit % = x%. Step 3: Selling Price (SP) = CP + Profit. Step 4: Profit = (Profit % / 100) × CP = (x/100) × x = x^2 / 100. Step 5: Set up the equation: SP = x + (x^2 / 100). Step 6: Given SP = Rs. 75, so 75 = x + (x^2 / 100). Step 7: Multiply by 100: 7500 = 100x + x^2. Step 8: Rearrange: x^2 + 100x - 7500 = 0. Step 9: Test options. If CP = Rs. 50, then Profit % = 50%. Step 10: Profit = 50% of 50 = Rs. 25. Step 11: SP = 50 + 25 = Rs. 75. This matches the given SP. Step 12: Therefore, the Cost Price is Rs. 50.
15
A shopkeeper states a selling price of Rs. 20 per kg for articles that cost him Rs. 23 per kg. However, he uses a defective scale, dispensing only 800 gm for every 1 kg claimed. What is his actual profit percentage?
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Solution: Step 1: Calculate the ratio of the declared selling price to the actual cost price per unit: 20/23. Step 2: Account for the false weight. The shopkeeper claims to sell 1000 gm but only gives 800 gm. This means for the actual quantity given (800 gm), he charges the price of 1000 gm. The weight factor is 1000/800. Step 3: Combine these factors to find the effective selling price to cost price ratio: Effective SP / Effective CP = (Declared SP / Actual CP per unit weight) * (Claimed Weight / Actual Weight given) Effective SP / Effective CP = (20 / 23) * (1000 / 800). Step 4: Simplify the ratio: (20 / 23) * (5 / 4) = 100 / 92 = 25 / 23. Step 5: If the effective Cost Price is 23 units, the effective Selling Price is 25 units. Step 6: Profit = 25 - 23 = 2 units. Step 7: Profit Percentage = (Profit / Effective CP) * 100 = (2 / 23) * 100 = 200 / 23 %. Step 8: Convert to mixed fraction: 200 / 23 % = 8 16/23 %.
16
If the selling price of an article is 32% more than its cost price, and the discount offered on its marked price is 12%, then what is the ratio of its cost price to the marked price?
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Solution: Step 1: Relate Cost Price (CP) to Selling Price (SP) using the profit information. * SP is 32% more than CP. This means CP:SP = 100:(100+32) = 100:132. Simplify to 25:33. Step 2: Relate Marked Price (MP) to Selling Price (SP) using the discount information. * Discount of 12% on MP. This means SP:MP = (100-12):100 = 88:100. Simplify to 22:25. Step 3: Combine these two ratios (CP:SP and SP:MP) to get a consolidated ratio CP:SP:MP. * To make the 'SP' part of the ratio consistent, find the Least Common Multiple (LCM) of 33 and 22, which is 66. * From CP:SP = 25:33, multiply by 2: (25*2):(33*2) = 50:66. * From SP:MP = 22:25, multiply by 3: (22*3):(25*3) = 66:75. * So, CP:SP:MP = 50:66:75. Step 4: The required ratio is Cost Price to Marked Price (CP:MP). Step 5: From the combined ratio, CP:MP = 50:75. Step 6: Simplify the ratio by dividing both sides by their greatest common divisor, 25: 2:3.
17
Raju purchased eggs at two different rates: initially, 3 eggs for a rupee, and later, an equal number of eggs at 6 eggs for a rupee. The next day, he sold all the eggs at a rate of 9 eggs for Rs. 2. What is his overall percentage profit or loss?
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Solution: Step 1: Calculate the cost price (CP) of one egg in the first purchase: Rs. 1 / 3 eggs = Rs. 1/3 per egg. Step 2: Calculate the CP of one egg in the second purchase: Rs. 1 / 6 eggs = Rs. 1/6 per egg. Step 3: Since an equal number of eggs were purchased in both instances, calculate the average CP per egg. Let's assume he bought 6 eggs at each rate (LCM of 3 and 6). Cost for first 6 eggs = Rs. 2 (6 eggs * Rs. 1/3). Cost for second 6 eggs = Rs. 1 (6 eggs * Rs. 1/6). Total eggs purchased = 6 + 6 = 12 eggs. Total cost = Rs. 2 + Rs. 1 = Rs. 3. Average CP per egg = Rs. 3 / 12 eggs = Rs. 1/4 per egg. Step 4: Calculate the selling price (SP) of one egg: Rs. 2 / 9 eggs = Rs. 2/9 per egg. Step 5: Compare the average CP and SP. CP = Rs. 1/4 (0.25) and SP = Rs. 2/9 (approx 0.2222). Since SP < CP, there is a loss. Step 6: Calculate the percentage loss: `((CP - SP) / CP) * 100`. `((1/4 - 2/9) / (1/4)) * 100 = ((9/36 - 8/36) / (1/4)) * 100` `= ((1/36) / (1/4)) * 100 = (1/36) * 4 * 100 = (1/9) * 100 = 11.11%`. Step 7: Raju incurs an 11.11% loss.
18
A book seller sells a book at a 10% profit. If he had purchased it at 4% less and sold it for Rs. 6 more, he would have gained 18 3/4%. What is the cost price of the book?
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Solution: Step 1: Let the original Cost Price (CP1) of the book be Rs. X. Step 2: Calculate the original Selling Price (SP1) with a 10% profit: SP1 = X + 0.10X = 1.10X. Step 3: In the new scenario, if he bought it at 4% less, the new Cost Price (CP2) would be X - 0.04X = 0.96X. Step 4: If he sold it for Rs. 6 more, the new Selling Price (SP2) would be SP1 + 6 = 1.10X + 6. Step 5: In this new scenario, the profit is 18 3/4% (which is 18.75% or 75/4%). Step 6: So, SP2 = CP2 + 18.75% of CP2 = CP2 * (1 + 0.1875) = 1.1875 * CP2. Step 7: Substitute the expressions for SP2 and CP2: 1.10X + 6 = 1.1875 * (0.96X). Step 8: Calculate the product on the right side: 1.1875 * 0.96 = 1.14 (approximately). (Alternatively, 0.96X * (1 + 75/400) = 0.96X * (1 + 3/16) = 0.96X * (19/16) = 0.06X * 19 = 1.14X). Step 9: Formulate the equation: 1.10X + 6 = 1.14X. Step 10: Rearrange to solve for X: 6 = 1.14X - 1.10X. Step 11: Simplify: 6 = 0.04X. Step 12: Solve for X: X = 6 / 0.04 = 600 / 4 = 150. Step 13: The cost price of the book is Rs. 150.
19
An article's marked price is 10% higher than its cost price. If a 10% discount is given on the marked price, what is the seller's outcome in this transaction?
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Solution: Step 1: Assume the Cost Price (CP) of the article is Rs. 100. Step 2: The Marked Price (MP) is 10% higher than the CP. So, MP = 100 + (10/100)*100 = Rs. 110. Step 3: A 10% discount is given on the MP. Calculate the Selling Price (SP): SP = MP * (100 - 10)/100 = 110 * 0.90 = Rs. 99. Step 4: Compare SP with CP. Since SP (Rs. 99) is less than CP (Rs. 100), there is a loss. Step 5: Calculate the Loss amount = CP - SP = 100 - 99 = Rs. 1. Step 6: Calculate the Loss percentage = (Loss amount / CP) * 100 = (1 / 100) * 100 = 1%. Conclusion: The seller bears a loss of 1%.
20
A tradesman offers a 15% discount on the marked price of his goods. To secure a 19% profit, by what percentage above the cost price must he mark his goods?
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Solution: Step 1: Identify the given percentages. Discount = 15% Profit = 19% Step 2: Use the relationship between Cost Price (CP), Marked Price (MP), Discount, and Profit. CP : MP = (100 - Discount%) : (100 + Profit%) Step 3: Substitute the given values. CP : MP = (100 - 15) : (100 + 19) CP : MP = 85 : 119 Step 4: Determine the difference between the Marked Price and Cost Price in terms of units. Difference = 119 - 85 = 34 units. Step 5: Calculate the percentage markup above the Cost Price. Percentage Markup = (Difference / CP) * 100 Percentage Markup = (34 / 85) * 100 Step 6: Simplify the calculation. Percentage Markup = (2 / 5) * 100 = 40%. Step 7: The tradesman must mark his goods 40% above the cost price.
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