The ratio of selling price to the cost price is 9 ∶ 8. What is the profit percentage?
12.5 percent
Let's solve this problem involving selling price, cost price, and profit percentage. We are given the ratio of the selling price to the cost price and need to find the profit percentage.
Understanding the Ratio of Selling Price to Cost Price
The question states that the ratio of selling price (SP) to the cost price (CP) is 9 ∶ 8. This means for every 9 units of selling price, the cost price is 8 units. We can represent this ratio mathematically as:
\(\frac{\text{Selling Price}}{\text{Cost Price}} = \frac{9}{8}\)
Calculating Profit from the Ratio
Since the selling price (9 units) is greater than the cost price (8 units), there is a profit. The profit is the difference between the selling price and the cost price.
\(\text{Profit} = \text{Selling Price} - \text{Cost Price}\)
Using the ratio values, we can think of SP = 9x and CP = 8x for some variable x. The profit would then be:
\(\text{Profit} = 9x - 8x = 1x\)
So, if CP is 8 units, the Profit is 1 unit.
Formula for Profit Percentage
The profit percentage is calculated based on the cost price. The formula is:
\(\text{Profit Percentage} = \frac{\text{Profit}}{\text{Cost Price}} \times 100\)
Step-by-Step Profit Percentage Calculation
Now, let's plug in the values we derived from the given ratio into the profit percentage formula.
From the ratio SP:CP = 9:8, we have Profit = 1 unit and Cost Price = 8 units.
\(\text{Profit Percentage} = \frac{1}{8} \times 100\)
To calculate this:
- Divide 100 by 8.
- \(100 \div 8 = 12.5\)
So, the profit percentage is 12.5 percent.
Summary of Calculation
| Item | Value (based on ratio) |
|---|---|
| Ratio SP : CP | 9 : 8 |
| Selling Price (SP) | 9 units |
| Cost Price (CP) | 8 units |
| Profit (SP - CP) | \(9 - 8 = 1\) unit |
| Profit Percentage | \(\frac{\text{Profit}}{\text{CP}} \times 100 = \frac{1}{8} \times 100\) |
| Result | 12.5 percent |
Therefore, the profit percentage is 12.5 percent.
Revision Table: Profit and Loss Concepts
| Concept | Definition | Formula |
|---|---|---|
| Cost Price (CP) | The price at which an article is purchased. | N/A |
| Selling Price (SP) | The price at which an article is sold. | N/A |
| Profit | When SP > CP. | Profit = SP - CP |
| Loss | When SP < CP. | Loss = CP - SP |
| Profit % | Profit calculated on CP in percentage. | \(\frac{\text{Profit}}{\text{CP}} \times 100\) |
| Loss % | Loss calculated on CP in percentage. | \(\frac{\text{Loss}}{\text{CP}} \times 100\) |
Additional Information: Working with Ratios
When dealing with ratios like Selling Price : Cost Price = 9 : 8, you can assume the values are 9x and 8x, where x is any positive number. However, for calculating percentages based on this ratio, the variable 'x' cancels out in the fraction, making it easy to use the ratio values directly as units.
For instance, if we used SP = 9x and CP = 8x:
Profit = 9x - 8x = x
Profit Percentage = \(\frac{x}{8x} \times 100 = \frac{1}{8} \times 100 = 12.5\%\)
This confirms that using the ratio numbers (9 and 8) directly for calculating percentage change relative to the base (CP) is correct and simplifies the process.
Important Questions from Profit and Loss
By selling an article for Rs. 2,200, a profit of 10% is earned. If the same article is sold for Rs. 2,600, then what will be the gain percentage?
By selling an article for Rs. 640, a person loses 15% of its selling price. At what price (in Rs.) should he sell it to gain 15% on its cost price?
The selling prices of articles A and B are the same. A is sold at a profit of 28 percent and B is sold at a loss of 24 percent. If the total selling price of the both articles is Rs. 48640, then what is the cost price of A and B, respectively ?
The cost price of an article is Rs. 2800. Profit as a percentage of selling price is 20 percent. What is the actual profit (in Rs.) ?
A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?
