A sold an article to B at 25% profit and B further sold it to C by earning a certain profit. If the cost price of C is 30% more than the cost price of A, then find the profit percentage earned by B.
4%
Calculating Profit Percentage Between Sellers
This problem involves calculating the profit percentage earned by an intermediate seller (B) in a chain of transactions, given the profit percentage of the first seller (A) and the relationship between the final buyer's cost price (C) and the original seller's cost price (A).
Step-by-Step Calculation
Let's assume the cost price of the article for A is \( \text{CP}_A \). We are given the following information:
- A sells to B at a 25% profit.
- B sells to C at a certain profit percentage (which we need to find). Let this be \( P_B \% \).
- The cost price for C is 30% more than the cost price for A.
1. Calculate the Cost Price for B (\( \text{CP}_B \))
A sold the article to B at a 25% profit. This means the selling price for A is the cost price for B.
\( \text{Selling Price}_A = \text{CP}_A + 25\% \text{ of } \text{CP}_A \)
\( \text{Selling Price}_A = \text{CP}_A + 0.25 \times \text{CP}_A \)
\( \text{Selling Price}_A = 1.25 \times \text{CP}_A \)
Since the selling price for A is the cost price for B:
\( \text{CP}_B = 1.25 \times \text{CP}_A \)
2. Calculate the Cost Price for C (\( \text{CP}_C \))
We are told that the cost price for C is 30% more than the cost price for A.
\( \text{CP}_C = \text{CP}_A + 30\% \text{ of } \text{CP}_A \)
\( \text{CP}_C = \text{CP}_A + 0.30 \times \text{CP}_A \)
\( \text{CP}_C = 1.30 \times \text{CP}_A \)
3. Determine the Selling Price for B
B sold the article to C. The cost price for C is the selling price for B.
\( \text{Selling Price}_B = \text{CP}_C \)
From step 2, we know \( \text{CP}_C = 1.30 \times \text{CP}_A \).
So, \( \text{Selling Price}_B = 1.30 \times \text{CP}_A \)
4. Calculate the Profit Earned by B
Profit earned by B is the difference between B's selling price and B's cost price.
\( \text{Profit}_B = \text{Selling Price}_B - \text{CP}_B \)
Substitute the values from steps 1 and 3:
\( \text{Profit}_B = (1.30 \times \text{CP}_A) - (1.25 \times \text{CP}_A) \)
\( \text{Profit}_B = (1.30 - 1.25) \times \text{CP}_A \)
\( \text{Profit}_B = 0.05 \times \text{CP}_A \)
5. Calculate the Profit Percentage Earned by B
The profit percentage is calculated based on the cost price of B.
\( P_B \% = \left( \frac{\text{Profit}_B}{\text{CP}_B} \right) \times 100 \)
Substitute the values from steps 1 and 4:
\( P_B \% = \left( \frac{0.05 \times \text{CP}_A}{1.25 \times \text{CP}_A} \right) \times 100 \)
The term \( \text{CP}_A \) cancels out:
\( P_B \% = \left( \frac{0.05}{1.25} \right) \times 100 \)
\( P_B \% = \left( \frac{5}{125} \right) \times 100 \)
\( P_B \% = \left( \frac{1}{25} \right) \times 100 \)
\( P_B \% = 4 \% \)
The profit percentage earned by B is 4%.
Summary of Transactions
| Party | Cost Price (relative to \(\text{CP}_A\)) | Selling Price (relative to \(\text{CP}_A\)) | Profit % |
|---|---|---|---|
| A | \( \text{CP}_A \) | \( 1.25 \times \text{CP}_A \) (\( \text{CP}_B \)) | 25% |
| B | \( 1.25 \times \text{CP}_A \) | \( 1.30 \times \text{CP}_A \) (\( \text{CP}_C \)) | \( \left( \frac{1.30 \times \text{CP}_A - 1.25 \times \text{CP}_A}{1.25 \times \text{CP}_A} \right) \times 100 = 4\% \) |
The profit percentage earned by B is 4%.
Revision Table: Key Concepts
| Concept | Formula | Description |
|---|---|---|
| Profit | \( \text{Profit} = \text{Selling Price} - \text{Cost Price} \) | Earned when Selling Price > Cost Price. |
| Profit Percentage | \( \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \) | Profit expressed as a percentage of the Cost Price. |
| Selling Price with Profit | \( \text{Selling Price} = \text{Cost Price} \times \left( 1 + \frac{\text{Profit Percentage}}{100} \right) \) | Formula to calculate SP when CP and Profit% are known. |
Additional Information on Profit and Loss Calculations
Profit and loss calculations are fundamental concepts in business mathematics. They help in understanding the profitability of transactions.
- The cost price is the initial price at which an item is bought.
- The selling price is the price at which an item is sold.
- If selling price is greater than cost price, there is a profit.
- If selling price is less than cost price, there is a loss.
- Profit or loss percentage is always calculated on the cost price unless otherwise specified.
- In a chain transaction, the selling price for one person becomes the cost price for the next person in the chain.
Understanding these basic principles is crucial for solving problems involving multiple sales stages and profit/loss calculations.
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