Understanding the Profit Percentage Problem

This problem involves calculating the profit percentage of a chair under different selling scenarios. We are given the selling price after a discount, the discount rate, and the cost price. We need to find the profit percentage if the chair is sold at its original marked price.

Calculating the Marked Price (MP)

The chair was sold for Rs. 720 after a 10% discount on the marked price. This means the selling price is 90% of the marked price.

Let MP be the marked price.

The selling price (SP) is given by:

\( \text{SP} = \text{MP} - \text{Discount} \)

The discount is 10% of the marked price, which can be written as \( 0.10 \times \text{MP} \).

So, the equation becomes:

\( 720 = \text{MP} - 0.10 \times \text{MP} \)

\( 720 = (1 - 0.10) \times \text{MP} \)

\( 720 = 0.90 \times \text{MP} \)

Now, we can find the marked price:

\( \text{MP} = \frac{720}{0.90} \)

\( \text{MP} = \frac{7200}{9} \)

\( \text{MP} = 800 \)

So, the marked price of the chair is Rs. 800.

Calculating Profit When Sold at Marked Price

We are given that the cost price (CP) of the chair is Rs. 640.

We want to find the profit percentage if the chair is sold at the marked price, which is Rs. 800.

When sold at the marked price, the selling price (SPnew) is equal to the marked price.

\( \text{SP}_{\text{new}} = \text{MP} = 800 \)

The profit is calculated as:

\( \text{Profit} = \text{SP}_{\text{new}} - \text{CP} \)

\( \text{Profit} = 800 - 640 \)

\( \text{Profit} = 160 \)

The profit when selling the chair at the marked price is Rs. 160.

Calculating the Profit Percentage

The profit percentage is calculated with respect to the cost price.

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

Using the values we found:

\( \text{Profit Percentage} = \left( \frac{160}{640} \right) \times 100 \)

Simplify the fraction:

\( \frac{160}{640} = \frac{16}{64} = \frac{1}{4} \)

Now, calculate the percentage:

\( \text{Profit Percentage} = \frac{1}{4} \times 100 \)

\( \text{Profit Percentage} = 25 \)

So, the profit percentage if the chair is sold at the marked price is 25%.

Revision Table: Key Concepts

Additional Information on Profit and Loss

Profit and loss calculations are fundamental in commercial arithmetic. Here are some important points:

• Profit or Loss is always calculated on the Cost Price (CP) unless otherwise specified.
• Discount is always calculated on the Marked Price (MP) unless otherwise specified.
• Selling Price (SP) = Cost Price (CP) + Profit.
• Selling Price (SP) = Cost Price (CP) - Loss.
• Selling Price (SP) = Marked Price (MP) - Discount.
• If SP > CP, there is a profit.
• If SP < CP, there is a loss.
• If SP = CP, there is neither profit nor loss.

Understanding the relationship between CP, SP, MP, Discount, and Profit/Loss is crucial for solving such problems.