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

To solve the problem, we need to find the cost price of the article given the selling price after discount and the profit percentage.

1. Understanding the Concepts:

- Discount: Reduction on the marked price.
- Selling Price (SP): Price after discount.
- Profit Percentage: Percentage increase over cost price.
- Cost Price (CP): The original price before profit.
- Relationship: \( \text{SP} = \text{CP} + \text{Profit} = \text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right) \)

2. Given Values:

- Selling price after 10% discount = Rs 1440
- Profit = 20%

3. Calculate the Marked Price (MP):

Discount = 10% → SP = 90% of MP
\[ 1440 = 0.9 \times \text{MP} \Rightarrow \text{MP} = \frac{1440}{0.9} = 1600 \]

4. Calculate the Cost Price (CP):

Profit = 20% → SP = 120% of CP
\[ \text{SP} = 1440 = 1.2 \times \text{CP} \Rightarrow \text{CP} = \frac{1440}{1.2} = 1200 \]

Final Answer:

The cost price of the article is Rs 1200.