Question

An article is sold for Rs 1440 after allowing a discount of 10%. If the profit made is 20%, find the cost price.

• A. Rs 1200
• B. Rs 1100
• C. Rs 1000
• D. Rs 1250

Hint:

In profit and loss problems, distinguish between marked price (MP), selling price (SP), and cost price (CP). Calculate the SP as a percentage of MP after discount ($SP = MP \times (1 - \text{discount\%})$) and as a percentage of CP after profit ($SP = CP \times (1 + \text{profit\%})$). Work backward from SP to find CP or MP, and verify by checking both discount and profit conditions.

Answer 1

The Correct Option is A

The objective is to determine the cost price of an article, given its selling price after a discount and the profit percentage achieved.

1. Conceptual Definitions:

- Discount: A reduction applied to the marked price.
- Selling Price (SP): The price of the article after the discount is applied.
- Profit Percentage: The percentage increase relative to the cost price.
- Cost Price (CP): The initial price of the article before any profit is added.
- Formula: \( \text{SP} = \text{CP} + \text{Profit} = \text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right) \)

2. Provided Information:

- Selling price after a 10% discount: Rs 1440
- Profit percentage: 20%

3. Marked Price Calculation (MP):

A 10% discount means the selling price is 90% of the marked price.
\[ 1440 = 0.9 \times \text{MP} \Rightarrow \text{MP} = \frac{1440}{0.9} = 1600 \]

4. Cost Price Calculation (CP):

A 20% profit means the selling price is 120% of the cost price.
\[ \text{SP} = 1440 = 1.2 \times \text{CP} \Rightarrow \text{CP} = \frac{1440}{1.2} = 1200 \]

Conclusion:

The cost price of the article is determined to be Rs 1200.