A man earns a profit of 35 percent by selling a chair for a certain price. If he sells that chair at double the price, then what will be the profit percentage?
170 percent
Calculating Profit Percentage After Doubling Selling Price
This problem involves understanding the relationship between Cost Price (CP), Selling Price (SP), Profit, and Profit Percentage. We are given an initial profit percentage and asked to find the new profit percentage when the selling price is doubled while the cost price remains constant.
Understanding Key Terms
- Cost Price (CP): The price at which an item is bought.
- Selling Price (SP): The price at which an item is sold.
- Profit: The difference between the Selling Price and the Cost Price when SP > CP (Profit = SP - CP).
- Profit Percentage: The profit expressed as a percentage of the Cost Price [Profit % = (Profit / CP) * 100].
Step-by-Step Calculation
Initial Scenario: 35% Profit
Let's assume the Cost Price (CP) of the chair is $\text{C}$.
The man earns a profit of 35 percent. This means the profit is 35% of the Cost Price.
Initial Profit Amount = 35% of CP = $\frac{35}{100} \times \text{C} = 0.35\text{C}$
The initial Selling Price (SP1) is the Cost Price plus the Profit Amount.
SP1 = CP + Initial Profit Amount
SP1 = $\text{C} + 0.35\text{C} = 1.35\text{C}$
New Scenario: Selling at Double the Price
The problem states that the chair is now sold at double the initial price. So, the new Selling Price (SP2) is twice the initial Selling Price (SP1).
SP2 = $2 \times \text{SP1}$
We found that SP1 = $1.35\text{C}$. Substituting this value:
SP2 = $2 \times 1.35\text{C} = 2.70\text{C}$
The Cost Price (CP) remains the same, which is $\text{C}$.
The new Profit (Profit2) is the new Selling Price minus the Cost Price.
Profit2 = SP2 - CP
Profit2 = $2.70\text{C} - \text{C} = 1.70\text{C}$
Calculating the New Profit Percentage
The new Profit Percentage is the new Profit divided by the Cost Price, multiplied by 100.
New Profit Percentage = $\frac{\text{Profit2}}{\text{CP}} \times 100$
New Profit Percentage = $\frac{1.70\text{C}}{\text{C}} \times 100$
The 'C' in the numerator and denominator cancels out.
New Profit Percentage = $1.70 \times 100 = 170$ percent.
So, if the chair is sold at double the initial price, the profit percentage will be 170 percent.
| Item | Value (in terms of CP) | Calculation/Notes |
|---|---|---|
| Initial Profit % | 35% | Given |
| Cost Price (CP) | $\text{C}$ | Assumed variable |
| Initial Profit Amount | $0.35\text{C}$ | 35% of CP |
| Initial Selling Price (SP1) | $1.35\text{C}$ | CP + Initial Profit Amount |
| New Selling Price (SP2) | $2.70\text{C}$ | $2 \times \text{SP1}$ |
| New Profit Amount (Profit2) | $1.70\text{C}$ | SP2 - CP |
| New Profit Percentage | 170% | (Profit2 / CP) * 100 |
Revision Table: Profit Calculation Summary
| Parameter | Initial Case | New Case (SP Doubled) |
|---|---|---|
| Cost Price (CP) | $\text{C}$ | $\text{C}$ |
| Profit Percentage | 35% | 170% |
| Profit Amount | $0.35\text{C}$ | $1.70\text{C}$ |
| Selling Price (SP) | $1.35\text{C}$ | $2.70\text{C}$ |
Additional Information: Relating Profit and Selling Price
This problem highlights how profit percentage changes drastically when the selling price is increased, especially when the cost price remains constant. The profit amount is directly proportional to the selling price (assuming fixed cost price). Consequently, the profit percentage, which is calculated relative to the cost price, will increase significantly when the selling price doubles or changes.
If the selling price doubles, the increase in selling price is equal to the original selling price (SP2 - SP1 = SP1). The new profit is the original profit plus this increase in selling price. Since the original selling price is significantly larger than the original profit (SP1 = CP + Profit1), doubling the selling price adds a large amount to the profit, leading to a much higher profit percentage relative to the (unchanged) cost price.
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