Profit Calculation Steps
This problem involves calculating the overall profit percentage (x%) based on different profit and loss margins applied to segments of goods sold during a sale.
Assume Total Goods and Cost Price
To simplify calculations, let's assume:
- Total quantity of goods = 100 units.
- Cost Price (CP) per unit = $1.
- Therefore, Total Cost Price = 100 units * $1/unit = $100$.
Calculate Sales Breakdown
The goods are divided into three groups based on selling conditions:
| Group | Quantity (Units) | CP ($) | Profit/Loss (%) | SP ($) |
|---|---|---|---|---|
| 1 (55%) | 55 | 55 | +41% | $77.55$ |
| 2 (20% of remaining) | 9 | 9 | +19% | $10.71$ |
| 3 (Rest) | 36 | 36 | -21% | $28.44$ |
Calculations for SP:
- Group 1 SP: Calculated as $\text{CP} \times (1 + \text{Profit\%})$. $\\$55 \times (1 + 0.41) = \$55 \times 1.41 = \$77.55$.
- Group 2 SP: Calculated similarly. $\\$9 \times (1 + 0.19) = \$9 \times 1.19 = \$10.71$.
- Group 3 SP: Calculated using the loss percentage. $\\$36 \times (1 - 0.21) = \$36 \times 0.79 = \$28.44$.
Calculate Total Selling Price and Overall Profit
Sum the selling prices (SP) of all groups to find the Total Selling Price (Total SP):
Total SP = SP Group 1 + SP Group 2 + SP Group 3
Total SP = $\$77.55 + \$10.71 + \$28.44 = \$116.70$.
Calculate the overall profit by subtracting the Total Cost Price (Total CP) from the Total SP:
Overall Profit = Total SP - Total CP = $\$116.70 - \$100 = \$16.70$.
Determine the Overall Profit Percentage (x)
Calculate the overall profit percentage using the standard formula:
Overall Profit % = $(\frac{\text{Overall Profit}}{\text{Total CP}}) \times 100\%
Substitute the calculated values:
x% = $(\frac{\$16.70}{\$100}) \times 100\% = 16.70\%$.
Therefore, the value of x is 16.70.
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, 50% of the goods are sold at a 49% profit, 32% of the remaining goods are sold at a 45% profit and the still remaining goods are sold at a loss of 15%. If there is an overall profit of x%, then what is the value of x?
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- 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?
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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?
