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Question 1 / 20
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An article, listed at Rs. 920, is purchased for Rs. 742.90 after two consecutive discounts. If the first discount was 15%, what was the percentage rate of the second discount?
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Solution: Step 1: Calculate the price after the first discount. - Listed Price (MP) = Rs. 920. - First Discount = 15% of 920 = Rs. 138. - Price after first discount = 920 - 138 = Rs. 782. Step 2: Calculate the amount of the second discount. - Final Selling Price (SP) = Rs. 742.90. - Amount of second discount = Price after first discount - Final SP = 782 - 742.90 = Rs. 39.10. Step 3: Calculate the percentage of the second discount. - The second discount is calculated on the price *after* the first discount (Rs. 782). - Second Discount Percentage = (Amount of second discount / Price after first discount) * 100 - Second Discount Percentage = (39.10 / 782) * 100 = 5%.
2
A dishonest merchant advertises a 12.5% loss on the cost price of his goods, but he substitutes a 28 g weight for a 36 g weight. What is his actual percentage profit or loss?
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Solution: Step 1: Let the cost price (CP) of 36 grams of goods be Rs. 36 (i.e., Rs. 1 per gram). Step 2: The merchant claims to sell at a 12.5% loss on CP. So, his stated selling price (SP_stated) for 36 grams would be 36 * (1 - 0.125) = 36 * 0.875 = Rs. 31.5. Step 3: However, he uses a 28 g weight instead of a 36 g weight. This means he actually gives 28 grams of goods. Step 4: The actual cost price for the quantity he sells (28 grams) is Rs. 28 (since CP is Rs. 1 per gram). Step 5: The actual selling price (SP_actual) for these 28 grams is Rs. 31.5 (what the customer paid). Step 6: Calculate the actual profit or loss: Profit = SP_actual - CP_actual = 31.5 - 28 = Rs. 3.5. Step 7: Since SP_actual > CP_actual, it's a profit. Step 8: Calculate the actual profit percentage: Profit % = (Profit / CP_actual) * 100 = (3.5 / 28) * 100. Step 9: Simplify: (3.5 / 28) = 1/8. So, Profit % = (1/8) * 100 = 12.5%. Step 10: His actual percentage profit is 12.5% gain.
3
When the price of tea is reduced by 10%, a dealer can buy an additional 25 kg of tea for Rs. 22500. Determine the new price per kg of tea.
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Solution: Step 1: Calculate the amount of money saved due to the 10% reduction on the total amount spent. Step 2: Money saved = 10% of Rs. 22500 = (10/100) * 22500 = Rs. 2250. Step 3: This saved amount (Rs. 2250) enables the dealer to purchase 25 kg more tea at the reduced price. Step 4: Calculate the reduced price per kg of tea: Reduced Price = Money Saved / Extra Quantity. Step 5: Reduced Price = Rs. 2250 / 25 kg = Rs. 90 per kg. Step 6: The reduced price per kg of tea is Rs. 90.
4
A manufacturer sources two components, A and B, from Country X and Country Y, contributing 30% and 50% to production costs, respectively. The product is sold at a 20% profit. Due to global changes, component costs rise by 30% and 22%, respectively. With a maximum selling price increase of 10%, what is the highest achievable profit percentage?
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Solution: Step 1: Assume total production cost = 100 units (A = 30, B = 50, other = 20) Step 2: Original selling price = 120 units (20% profit) Step 3: New cost of A = 30 * 1.3 = 39 units Step 4: New cost of B = 50 * 1.22 = 61 units Step 5: New total cost = 39 + 61 + 20 = 120 units Step 6: Maximum new selling price = 120 * 1.1 = 132 units Step 7: New profit = 132 - 120 = 12 units Step 8: Profit percentage = (12 / 120) * 100 = 10%
5
A bicycle, initially marked at Rs. 2,000, is subject to successive discounts of 20% and 10%. An extra 5% discount is provided for cash payments. What is the final selling price of the bicycle when paid in cash?
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Solution: Step 1: Calculate the price after the first discount. - Marked Price (MP) = Rs. 2,000. - First Discount = 20% of 2,000 = Rs. 400. - Price after first discount = 2,000 - 400 = Rs. 1,600. Step 2: Calculate the price after the second discount. - Second Discount = 10% of Rs. 1,600 = Rs. 160. - Price after second discount = 1,600 - 160 = Rs. 1,440. Step 3: Calculate the final selling price after the cash discount. - Cash Discount = 5% of Rs. 1,440 = Rs. 72. - Final Selling Price = 1,440 - 72 = Rs. 1,368.
6
Srinivas sold an article for Rs. 6800, incurring a loss. If he had sold it for Rs. 7850, his profit would have been half the original loss amount. At what price should he sell the article to achieve a 20% profit?
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Solution: Step 1: Let the Cost Price (CP) of the article be 'x'. Step 2: When sold for Rs. 6800, a loss is incurred. Loss = CP - SP1 = x - 6800. Step 3: When sold for Rs. 7850, a profit is earned. Profit = SP2 - CP = 7850 - x. Step 4: According to the problem, the profit is half the loss: (7850 - x) = (x - 6800) / 2. Step 5: Multiply both sides by 2: 2(7850 - x) = x - 6800. Step 6: Expand: 15700 - 2x = x - 6800. Step 7: Gather x terms on one side and constants on the other: 15700 + 6800 = x + 2x. Step 8: Simplify: 22500 = 3x. Step 9: Solve for x: x = 22500 / 3 = 7500. So, the Cost Price (CP) is Rs. 7500. Step 10: To achieve a 20% profit, the desired Selling Price (SP_target) = CP × (100 + 20)/100. Step 11: SP_target = 7500 × (120/100) = 7500 × 1.20 = Rs. 9000.
7
The profit percentage on three articles A, B, and C is 10%, 20%, and 25% respectively. The ratio of their cost prices is 1:2:4. If the ratio of the number of articles sold of A, B, and C is 2:5:2, what is the overall profit percentage?
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Solution: Step 1: Assign symbolic values based on the given ratios. Let the unit Cost Prices be: CP_A = `x`, CP_B = `2x`, CP_C = `4x`. Let the number of articles sold be: Quantity_A = `2y`, Quantity_B = `5y`, Quantity_C = `2y`. Step 2: Calculate the Total Cost Price for each article category: Total CP_A = `x * 2y = 2xy`. Total CP_B = `2x * 5y = 10xy`. Total CP_C = `4x * 2y = 8xy`. Step 3: Calculate the Profit earned from each article category: Profit_A = 10% of Total CP_A = 0.10 * 2xy = 0.2xy. Profit_B = 20% of Total CP_B = 0.20 * 10xy = 2xy. Profit_C = 25% of Total CP_C = 0.25 * 8xy = 2xy. Step 4: Calculate the Overall Total Cost Price: Overall Total CP = Total CP_A + Total CP_B + Total CP_C = 2xy + 10xy + 8xy = 20xy. Step 5: Calculate the Overall Total Profit: Overall Total Profit = Profit_A + Profit_B + Profit_C = 0.2xy + 2xy + 2xy = 4.2xy. Step 6: Calculate the Overall Profit Percentage: Overall Profit % = `(Overall Total Profit / Overall Total CP) * 100`. `= (4.2xy / 20xy) * 100 = (4.2 / 20) * 100 = 0.21 * 100 = 21%`.
8
An article is sold for Rs. 1920, resulting in a percentage profit equal to the percentage loss incurred if the same article were sold for Rs. 1280. At what price must the article be sold to achieve a 25% profit?
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Solution: Step 1: Let the Cost Price (C.P.) of the article be Rs. 'x'. Step 2: When S.P. = Rs. 1920, Profit = 1920 - x. Profit % = [(1920 - x) / x] * 100. Step 3: When S.P. = Rs. 1280, Loss = x - 1280. Loss % = [(x - 1280) / x] * 100. Step 4: Given that Profit % = Loss %. Step 5: [(1920 - x) / x] * 100 = [(x - 1280) / x] * 100. Step 6: Since x (C.P.) cannot be zero, we can cancel 'x' and '100' from both sides: 1920 - x = x - 1280. Step 7: Rearrange to solve for x: 1920 + 1280 = x + x. Step 8: 3200 = 2x. Step 9: x = 3200 / 2 = Rs. 1600. So, the C.P. of the article is Rs. 1600. Step 10: Now, calculate the Selling Price (S.P.) required to make a 25% profit. Step 11: Desired S.P. = C.P. * (100 + Profit %) / 100. Step 12: Desired S.P. = 1600 * (100 + 25) / 100 = 1600 * 125 / 100. Step 13: Desired S.P. = 16 * 125 = Rs. 2000.
9
A merchant purchases an article for Rs. 27. He then sells it, making a profit that is 10% of its selling price. Calculate the selling price of the article.
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Solution: Step 1: Let the Selling Price (SP) be 'x' Rs. Step 2: The Cost Price (CP) is given as Rs. 27. Step 3: Profit is 10% of the Selling Price, so Profit = 0.10x. Step 4: We know that SP = CP + Profit. Step 5: Substitute the values: x = 27 + 0.10x. Step 6: Rearrange the equation: x - 0.10x = 27. Step 7: 0.90x = 27. Step 8: Solve for x: x = 27 / 0.90. Step 9: x = 30. Step 10: The selling price of the article is Rs. 30.
10
If there is a 20% loss, what fraction should the selling price be multiplied by to obtain the cost price?
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Solution: Step 1: Let the Cost Price (CP) of the article be 'CP'. Step 2: A 20% loss means the Selling Price (SP) is 100% - 20% = 80% of the Cost Price. SP = 0.80 × CP. Step 3: We need to find a fraction 'k' such that CP = k × SP. Step 4: Substitute the expression for SP from Step 2 into the equation from Step 3. CP = k × (0.80 × CP). Step 5: Divide both sides by CP (assuming CP is not zero): 1 = k × 0.80. Step 6: Solve for k. k = 1 / 0.80 = 1 / (4/5) = 5/4. Step 7: The selling price must be multiplied by 5/4 to get the cost price.
11
Determine the single discount percentage that is equivalent to three consecutive discounts of 10%, 12%, and 5%.
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Solution: Step 1: First, calculate the equivalent discount for the first two discounts (10% and 12%). Step 2: Use the formula for equivalent discount: D_eq = (A + B - (A*B)/100)%. Step 3: D_eq(10, 12) = (10 + 12 - (10 * 12)/100)% = (22 - 120/100)% = (22 - 1.2)% = 20.8%. Step 4: Now, calculate the single equivalent discount for D_eq(10, 12) (20.8%) and the third discount (5%). Step 5: D_eq(Total) = (20.8 + 5 - (20.8 * 5)/100)%. Step 6: D_eq(Total) = (25.8 - 104/100)% = (25.8 - 1.04)% = 24.76%. Step 7: The single equivalent discount is 24.76%.
12
A shopkeeper applies two consecutive discounts to an article marked at Rs. 450. The first discount is 10%. If the customer pays Rs. 344.25 for the article, what was the percentage of the second discount?
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Solution: Step 1: Marked Price (MP) of the article = Rs. 450. Step 2: Price after the first 10% discount = 450 * (1 - 0.10) = 450 * 0.90 = Rs. 405. Step 3: The final amount paid by the customer (Selling Price, SP) = Rs. 344.25. Step 4: The amount of the second discount = Price after first discount - Final SP = 405 - 344.25 = Rs. 60.75. Step 5: The second discount percentage = (Amount of second discount / Price after first discount) * 100. Step 6: Second discount percentage = (60.75 / 405) * 100 = 15%. Step 7: The second discount given is 15%.
13
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.
14
A book vendor sold a book incurring a 10% loss. If he had sold it for Rs. 108 more, he would have achieved a 10% profit. Calculate the cost price of the book.
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Solution: Step 1: Let the Cost Price (CP) of the book be 'x'. Step 2: In the first scenario, there's a 10% loss. So, SP1 = x - 0.10x = 0.90x. Step 3: In the second scenario, there's a 10% profit. So, SP2 = x + 0.10x = 1.10x. Step 4: The difference between SP2 and SP1 is Rs. 108. So, 1.10x - 0.90x = 108. Step 5: Simplify the equation: 0.20x = 108. Step 6: Solve for x: x = 108 / 0.20 = 1080 / 2 = 540. Step 7: The cost price of the book is Rs. 540.
15
A shopkeeper announces selling cloth at a 4% loss. However, by using a faulty meter scale, he actually gains 20%. What is the true length of the scale he uses (in cm)?
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Solution: Step 1: Let the true length of the scale be 100 cm (representing 1 meter). Let 'L' be the actual length of the faulty scale in cm. Step 2: Assume the Cost Price (CP) of 100 cm of cloth is Rs. 100. Step 3: The shopkeeper advertises a 4% loss. So, he claims to sell 100 cm for: Declared Selling Price (SP) = CP - 4% of CP = 100 - 4 = Rs. 96. Step 4: However, he actually gains 20%. This gain is on the actual cost of the quantity of cloth he delivers (L cm). Let CP_L be the cost of L cm of cloth. CP_L = (L/100) * 100 = Rs. L. Actual Selling Price (SP_actual) for L cm of cloth = CP_L * (1 + 0.20) = L * 1.20 = 1.20L. Step 5: Since he sells L cm of cloth while charging for 100 cm, the amount he receives is Rs. 96 (his declared SP for 100 cm). So, SP_actual = 96. Step 6: Equate the actual selling price from Step 4 and Step 5. 1.20L = 96 Step 7: Solve for L. L = 96 / 1.20 L = 9600 / 120 L = 80 cm. Step 8: The actual length of the scale he uses is 80 cm.
16
A shopkeeper sells rice, claiming a 10% profit, but utilizes a weight that is 30% less than the actual measure. What is his overall gain percentage?
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Solution: Step 1: Assume the Cost Price (CP) of 1 kg (1000 gm) of rice = Rs. 100. Step 2: The shopkeeper claims a 10% profit, so the declared Selling Price (SP) for 1 kg *appears* to be Rs. 100 + 10% of 100 = Rs. 110. Step 3: However, the shopkeeper uses 30% less weight, meaning he actually gives only 1000 gm × (1 - 0.30) = 700 gm of rice for the price of 1 kg. Step 4: The actual cost price for the shopkeeper for the 700 gm he delivers is (700 / 1000) × 100 = Rs. 70. Step 5: The actual Selling Price (what the customer pays for 700 gm) is Rs. 110 (the declared price for 1 kg). Step 6: Calculate the actual Profit = Actual SP - Actual CP = 110 - 70 = Rs. 40. Step 7: Calculate the Actual Gain Percentage = (Actual Profit / Actual CP) × 100. Step 8: Substitute the values: (40 / 70) × 100 = (4 / 7) × 100 = 400 / 7 % = 57 1/7%.
17
A shopkeeper expects a 22.5% gain on his cost price. If his total sales for a week amounted to Rs. 392, what was his actual profit?
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Solution: Step 1: Let the Cost Price (CP) be x. Step 2: The Selling Price (SP) is CP + 22.5% of CP, which means SP = CP * (1 + 22.5/100) = CP * (122.5/100). Step 3: Given SP = Rs. 392. So, 392 = CP * (122.5 / 100). Step 4: Calculate CP: CP = 392 * (100 / 122.5) = 392 * (1000 / 1225) = Rs. 320. Step 5: The Cost Price (CP) of the sales was Rs. 320. Step 6: Profit = Selling Price - Cost Price = 392 - 320 = Rs. 72.
18
When an article is sold for Rs. 123.40, the profit achieved is 20% greater than the loss incurred if the article were sold for Rs. 108. If the article is instead sold for Rs. 120.75, what is the resulting gain or loss percentage?
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Solution: Step 1: Let the cost price of the article be CP. Step 2: If sold for Rs. 123.40, the gain (Profit) = 123.40 - CP. Step 3: If sold for Rs. 108, the loss = CP - 108. Step 4: Given that the gain is 20% more than the loss. Profit = Loss * (1 + 20/100) = Loss * 1.20. Step 5: Substitute the expressions for Profit and Loss into the equation: 123.40 - CP = 1.20 * (CP - 108). Step 6: Solve for CP: 123.40 - CP = 1.20 CP - 129.60. 123.40 + 129.60 = 1.20 CP + CP. 253.00 = 2.20 CP. CP = 253.00 / 2.20 = 2530 / 22 = Rs. 115. Step 7: Now, determine the gain or loss if the article is sold for Rs. 120.75. New Selling Price (NSP) = Rs. 120.75. Since NSP (120.75) is greater than CP (115), it is a gain. Gain = NSP - CP = 120.75 - 115 = Rs. 5.75. Step 8: Calculate the gain percentage. Gain % = (Gain / CP) * 100 = (5.75 / 115) * 100. Gain % = (575 / 11500) * 100 = 575 / 115 = 5%. Therefore, it is a Gain of 5%.
19
If an article is sold at a 200 percent profit, what will be the ratio of its cost price to its selling price?
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Solution: Step 1: Let the Cost Price (CP) of the article be Rs. 'x'. Step 2: Given that the Profit is 200% of the Cost Price. Step 3: Profit amount = (200/100) * x = 2x. Step 4: Selling Price (SP) = Cost Price + Profit = x + 2x = 3x. Step 5: The required ratio of Cost Price to Selling Price (CP : SP) = x : 3x. Step 6: Simplify the ratio: 1 : 3.
20
A fruit seller sells mangoes at the rate of Rs. 9 per kg, resulting in a 20% loss. At what price per kg should he sell them to make a profit of 5%?
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Solution: Step 1: The current selling price of Rs. 9 per kg corresponds to (100% - 20%) = 80% of the Cost Price (CP). Step 2: Let the new selling price be Rs. X per kg, which will correspond to (100% + 5%) = 105% of the Cost Price (CP). Step 3: Set up a direct proportion between selling prices and their corresponding percentage of CP: SP1 / (100 - Loss%) = SP2 / (100 + Gain%). Step 4: Substitute the given values: 9 / 80 = X / 105. Step 5: Solve for X: X = (9 * 105) / 80. Step 6: Perform the calculation: X = 945 / 80 = 11.8125. Step 7: Therefore, he should sell the mangoes at approximately Rs. 11.81 per kg to make a 5% profit.
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