Solving Profit and Loss Problems: Calculating Required Selling Price

This question asks us to find the selling price needed to achieve a 10% profit, given that the item was initially sold at a loss (43% below cost price).

Let's break down the information given:

• The initial selling price of the tea-set was Rs. 3,420.
• This selling price was 43% below the original cost price.

When something is sold 43% below the cost price, it means the selling price is (100 - 43)% of the cost price.

So, the initial selling price (Rs. 3,420) is 57% of the cost price.

We can represent this relationship mathematically:

\( \text{Selling Price} = \text{Cost Price} \times \left( \frac{100 - \text{Loss Percentage}}{100} \right) \)

In this case:

\( 3420 = \text{Cost Price} \times \left( \frac{100 - 43}{100} \right) \)

\( 3420 = \text{Cost Price} \times \left( \frac{57}{100} \right) \)

Now, we can calculate the original cost price (CP):

\( \text{Cost Price} = \frac{3420 \times 100}{57} \)

\( \text{Cost Price} = \frac{342000}{57} \)

Performing the division:

\( \text{Cost Price} = 6000 \)

So, the original cost price of the tea-set was Rs. 6,000.

The question asks what the selling price should have been to make a profit of 10%.

To make a profit of 10%, the selling price must be 10% more than the cost price. This means the selling price will be (100 + 10)% of the cost price.

So, the required selling price for a 10% profit is 110% of the cost price.

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

Using the calculated cost price (Rs. 6,000) and the desired profit percentage (10%):

\( \text{Required Selling Price} = 6000 \times \left( \frac{100 + 10}{100} \right) \)

\( \text{Required Selling Price} = 6000 \times \left( \frac{110}{100} \right) \)

\( \text{Required Selling Price} = 6000 \times 1.10 \)

\( \text{Required Selling Price} = 6600 \)

Therefore, to make a profit of 10%, the seller should have sold the tea-set for Rs. 6,600.

Revision Table: Key Concepts in Profit & Loss

Additional Information: Calculating Selling Price and Cost Price

The formulas for calculating selling price and cost price based on percentage profit or loss are very important:

• If there is a Profit of P%:
  • Selling Price \( = \text{CP} \times \left( \frac{100 + P}{100} \right) \)
  • Cost Price \( = \text{SP} \times \left( \frac{100}{100 + P} \right) \)
• If there is a Loss of L%:
  • Selling Price \( = \text{CP} \times \left( \frac{100 - L}{100} \right) \)
  • Cost Price \( = \text{SP} \times \left( \frac{100}{100 - L} \right) \)

In this problem, we first used the loss formula to find the Cost Price from the initial Selling Price and loss percentage. Then, we used the profit formula to find the new Selling Price based on the calculated Cost Price and desired profit percentage. Understanding these relationships is key to solving profit and loss problems.