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
Rohit buys 8 pens and 4 pencils for Rs. 2400. He sells pencils at a profit of 20 percent and pens at the loss of 10 percent. If his overall profit is Rs. 240, then what is the sum of the cost price of one pen and one pencil?
A man sells a car to his friend at the loss of 10 %; who in return sells it for Rs. 54000 making a profit of 20 %. What was the initial value of the car?
An article was sold at a loss of 24%. If it were sold for Rs. 1,596 more, then there would have been a gain of 18%, The cost price of the article is:
The cost price of an article is Rs.6,450. If it sold at a profit 16%, how much would be its selling price?
If the selling price of 7 articles is equal to the cost price of 6 articles, then what is the percentage loss?
