26.6%
Sale Profit Calculation: Overall Percentage
This solution details the calculation for the overall profit percentage ($x\%$) based on the conditions of a sale involving goods sold at different profit and loss margins.
Step-by-Step Calculation
To find the overall profit percentage, let's assume the total Cost Price (CP) of all goods is $100$. We will calculate the Selling Price (SP) for each portion of the goods sold.
Portion 1: Goods Sold at 49% Profit
- Cost Price (CP1): $50\%$ of $100 = 50$.
- Profit: $49\%$ of $50 = 0.49 \times 50 = 24.5$.
- Selling Price (SP1): $CP1 + \text{Profit} = 50 + 24.5 = 74.5$.
Portion 2: Remaining Goods Sold at 45% Profit
- Goods remaining after Portion 1: $100 - 50 = 50$.
- Cost Price for this portion (CP2): $32\%$ of the remaining $50 = 0.32 \times 50 = 16$.
- Profit: $45\%$ of $16 = 0.45 \times 16 = 7.2$.
- Selling Price (SP2): $CP2 + \text{Profit} = 16 + 7.2 = 23.2$.
Portion 3: Still Remaining Goods Sold at 15% Loss
- Goods remaining after Portions 1 and 2: $50 - 16 = 34$.
- Cost Price for this portion (CP3): $34$.
- Loss: $15\%$ of $34 = 0.15 \times 34 = 5.1$.
- Selling Price (SP3): $CP3 - \text{Loss} = 34 - 5.1 = 28.9$.
Overall Profit Determination
Now, we sum up the costs and selling prices to find the overall profit.
- Total Cost Price (Total CP): $CP1 + CP2 + CP3 = 50 + 16 + 34 = 100$.
- Total Selling Price (Total SP): $SP1 + SP2 + SP3 = 74.5 + 23.2 + 28.9 = 126.6$.
- Total Profit: Total SP - Total CP = $126.6 - 100 = 26.6$.
The overall profit percentage ($x\%$) is calculated as:
- $x\% = \left( \frac{\text{Total Profit}}{\text{Total CP}} \right) \times 100\)
- $x\% = \left( \frac{26.6}{100} \right) \times 100 = 26.6\%$.
Thus, the value of $x$ is $26.6$.
Similar Questions
A trader marks an article 25% above its cost price. He allows a discount of 10% on the marked price. After giving the discount, he makes a profit of ₹180 on the article. What is the cost price of the article?
A shopkeeper marks a product 75% above cost price and offers two successive discounts of 30% and 40%. What is the profit or loss percentage?
A trader buys 187 pens at ₹23 each. During transportation, 7 pens get damaged and cannot be sold. He sells the remaining pens at ₹27 each. Find his profit percentage. (rounded off to one decimal place)
A dealer buys a table for ₹2,750. He first marks it up by 28%, then allows a 12% discount to a customer. If the customer also pays 5% GST on the selling price, find the profit percentage (excluding GST) made by the dealer.
- During a sale, 55% of the goods are sold at a 41% profit, 20% of the remaining goods are sold at a 19% profit and the rest are sold at a 21% loss. If there is an overall profit of x%, then what is the value of x?
- During a sale, 40% of the goods are sold at a 44% profit, 25% of the remaining goods are sold at a 29% profit and the rest are sold at a 39% loss. If there is an overall profit of x%, then what is the value of x?
- The marked price of an item is 10% higher than the cost price and a discount of 10% is given on the marked price. What is the percentage gain or loss to the business owner in this sale?
- An article was sold for ₹ 576 when its cost price was ₹ 600. What is the percentage loss?
- The rate of discount on an article whose marked price is ₹ 170 and selling price is ₹ 130 is:
- A shopkeeper purchased some eggs at ₹ 19.20 per dozen and sold them at a profit of 25%. What is the selling price per egg?
Important Questions from Profit and Loss
Ram bought a chair at 35% discount on its market price, Had Ram got no discount, he would have had to pay ₹245 more. How much did Ram pay for the chair?
A shopkeeper bought an item for Rs. 4,500 and sold it at a loss of 5%. From this money, he bought another item and sold it at a profit of 10%. What is his overall profit?
A man sells two articles at Rs. 9,180 each. He gains 8% on one article and loses 15% on the other. His overall profit or loss is:
A shopkeeper selling an article for ₹46 loses 8%. In order to gain 6%, what should be the selling price of the article?
Rahul purchased 80 items from the market. 25% items of the total items were defective and the remaining items were sold at 50% profit. What will be the overall profit percentage?
