Finding the Cost Price with Discount and Profit

This problem involves understanding the relationship between Cost Price (CP), Selling Price (SP), Marked Price (MP), discount, and profit percentage. We are given a scenario where if a discount is offered on the marked price, a certain profit is made. We need to find the original cost price of the article.

Let's break down the information provided:

• An article was sold for Rs. 12,000. This price is likely the Marked Price (MP) from which the hypothetical discount is offered, as this interpretation allows us to connect the given numbers logically to the profit condition. So, let's assume the Marked Price (MP) is Rs. 12,000.
• Had a discount of 15% been offered (on the MP), a profit of 2% would have been made.

Let's calculate the Selling Price (SP) in the hypothetical scenario where a 15% discount is offered on the Marked Price (MP).

Discount amount = 15% of MP

\[\text{Discount amount} = \frac{15}{100} \times 12000\]

\[\text{Discount amount} = 15 \times 120\]

\[\text{Discount amount} = \text{Rs. } 1800\]

The Selling Price (SP) after the discount (let's call it SP') would be:

\[\text{SP'} = \text{MP} - \text{Discount amount}\]

\[\text{SP'} = 12000 - 1800\]

\[\text{SP'} = \text{Rs. } 10200\]

Now, we are told that if the article was sold at this price (SP' = Rs. 10200), a profit of 2% would have been made. Profit percentage is always calculated on the Cost Price (CP).

Profit = 2% of CP

\[\text{Profit} = \frac{2}{100} \times \text{CP}\]

The Selling Price (SP) is also related to Cost Price (CP) and Profit:

\[\text{SP} = \text{CP} + \text{Profit}\]

Using the values from the hypothetical scenario (SP' and 2% profit):

\[\text{SP'} = \text{CP} + \text{2% of CP}\]

\[10200 = \text{CP} + \frac{2}{100} \times \text{CP}\]

\[10200 = \text{CP} \left( 1 + \frac{2}{100} \right)\]

\[10200 = \text{CP} \left( \frac{100 + 2}{100} \right)\]

\[10200 = \text{CP} \left( \frac{102}{100} \right)\]

Now, we can solve for CP:

\[\text{CP} = 10200 \times \frac{100}{102}\]

We can simplify this calculation:

\[\text{CP} = \frac{1020000}{102}\]

Since \(102 \times 100 = 10200\), we can see that \(10200 / 102 = 100\).

\[\text{CP} = 100 \times 100\]

\[\text{CP} = \text{Rs. } 10000\]

Therefore, the cost price of the article was Rs. 10,000.

Let's verify this: If CP = Rs. 10,000 and MP = Rs. 12,000, a 15% discount on MP is Rs. 1800. The selling price after discount is Rs. 12000 - Rs. 1800 = Rs. 10200. The profit is Rs. 10200 - Rs. 10000 = Rs. 200. The profit percentage is (200 / 10000) * 100 = 2%. This matches the condition given in the problem.

Calculation Summary

Revision Table: Key Terms in Profit and Loss

Additional Information on Profit, Loss, and Discount Calculations

Understanding how discount affects the selling price is crucial in these types of problems. A discount is typically a percentage reduction on the Marked Price. The resulting price is the Selling Price for that transaction. Profit or Loss is then determined by comparing this Selling Price to the Cost Price.

• When a discount of R% is given on MP, the Selling Price (SP) is calculated as: \[\text{SP} = \text{MP} \times \left( \frac{100 - \text{R}}{100} \right)\]
• When there is a profit of P% on CP, the Selling Price (SP) is calculated as: \[\text{SP} = \text{CP} \times \left( \frac{100 + \text{P}}{100} \right)\]
• When there is a loss of L% on CP, the Selling Price (SP) is calculated as: \[\text{SP} = \text{CP} \times \left( \frac{100 - \text{L}}{100} \right)\]

In this problem, we used the first two formulas by equating the hypothetical selling price calculated using the discount on MP to the selling price calculated using the profit on CP.

Hypothetical SP = MP \(\times\) (100 - 15)/100 = \(12000 \times 0.85 = 10200\).

Hypothetical SP = CP \(\times\) (100 + 2)/100 = CP \(\times\) 1.02.

Equating them: \(10200 = \text{CP} \times 1.02\).

Solving for CP: \(\text{CP} = \frac{10200}{1.02} = 10000\).

This confirms our step-by-step calculation and reinforces the concepts.