Understanding the Profit and Loss Problem

This problem involves calculating the required profit percentage on one item when the cost prices, profit percentage on another item, and the desired overall profit percentage on the total transaction are known. We need to find out what profit percentage Radha should achieve on the Centre table to make an overall profit of 10%.

Step-by-Step Calculation for Overall Profit

First, let's determine the total cost price and the desired total selling price for the entire transaction.

• Cost Price of Computer table = Rs. 10000
• Cost Price of Centre table = Rs. 5000
• Total Cost Price = Cost of Computer table + Cost of Centre table

Total Cost Price \( = 10000 + 5000 = \text{Rs. } 15000 \)

The desired overall profit is 10% on the total transaction.

• Desired Total Profit Amount = 10% of Total Cost Price

Desired Total Profit Amount \( = \frac{10}{100} \times 15000 = 0.10 \times 15000 = \text{Rs. } 1500 \)

The desired total selling price for both tables combined is the total cost price plus the desired total profit.

• Desired Total Selling Price = Total Cost Price + Desired Total Profit Amount

Desired Total Selling Price \( = 15000 + 1500 = \text{Rs. } 16500 \)

Calculating Profit and Selling Price of Computer Table

Radha sold the Computer table with an 8% profit. Let's calculate the profit amount and its selling price.

• Cost Price of Computer table = Rs. 10000
• Profit Percentage on Computer table = 8%

Profit Amount on Computer table \( = \frac{8}{100} \times 10000 = 0.08 \times 10000 = \text{Rs. } 800 \)

Selling Price of Computer table \( = \text{Cost Price} + \text{Profit Amount} \)

Selling Price of Computer table \( = 10000 + 800 = \text{Rs. } 10800 \)

Finding the Required Selling Price and Profit for Centre Table

We know the desired total selling price for both tables and the actual selling price of the Computer table. We can find the required selling price for the Centre table.

• Required Selling Price of Centre table = Desired Total Selling Price - Selling Price of Computer table

Required Selling Price of Centre table \( = 16500 - 10800 = \text{Rs. } 5700 \)

Now we have the cost price and the required selling price for the Centre table. We can calculate the profit made on the Centre table.

• Cost Price of Centre table = Rs. 5000
• Required Selling Price of Centre table = Rs. 5700

Profit on Centre table \( = \text{Selling Price} - \text{Cost Price} \)

Profit on Centre table \( = 5700 - 5000 = \text{Rs. } 700 \)

Calculating the Profit Percentage on Centre Table

Finally, we can calculate the profit percentage on the Centre table using the profit amount and the cost price of the Centre table.

Profit Percentage \( = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \)

Profit Percentage on Centre table \( = \left( \frac{700}{5000} \right) \times 100 \)

Profit Percentage on Centre table \( = \left( \frac{7}{50} \right) \times 100 \)

Profit Percentage on Centre table \( = 7 \times 2 = 14\% \)

Therefore, Radha should sell the Centre table with a 14% profit to achieve a 10% profit on the whole transaction.

Revision Table: Key Figures

Additional Information on Profit and Loss

Profit and loss calculations are fundamental concepts in commercial arithmetic. Understanding these concepts is crucial for analyzing business transactions.

• Cost Price (CP): The price at which an article is purchased.
• Selling Price (SP): The price at which an article is sold.
• Profit: Occurs when SP > CP. Profit = SP - CP.
• Loss: Occurs when SP < CP. Loss = CP - SP.
• Profit Percentage: Calculated on the cost price. Profit % \( = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \).
• Loss Percentage: Calculated on the cost price. Loss % \( = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \).
• Overall Profit/Loss: Calculated based on the total cost price and total selling price of all items involved in a transaction.

These formulas and definitions help in solving various problems related to buying and selling goods.