Question

A shopkeeper marks an article 40% above its cost price and allows a discount of 10% on the marked price. If the article is sold for Rs 1,260, what is its cost price?

• A. Rs 1,000
• B. Rs 1,050
• C. Rs 1,100
• D. Rs 1,200

Hint:

To solve markup and discount questions quickly, you can use the effective percentage change formula:
\[ \text{Net Profit Percentage} = M - D - \frac{M \times D}{100} \]
Where \(M\) is the markup percentage (40%) and \(D\) is the discount percentage (10%).
\[ \text{Net Profit} = 40 - 10 - \frac{40 \times 10}{100} = 30 - 4 = 26% \]
Since there is a 26% profit, the selling price is 126% of the cost price.
Therefore, \(1.26 \times CP = 1260 \implies CP = 1000\).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The objective of this question is to determine the original cost price of an article given its markup percentage, discount percentage, and the final selling price.
We need to establish the relationship between the Cost Price (CP), Marked Price (MP), and Selling Price (SP).

Step 2: Key Formula or Approach:
Let the Cost Price of the article be represented as \(CP\).
The Marked Price is calculated by adding the markup percentage to the Cost Price:
\[ MP = CP \times \left(1 + \frac{\text{Markup %}}{100}\right) \]
The Selling Price is calculated by subtracting the discount percentage from the Marked Price:
\[ SP = MP \times \left(1 - \frac{\text{Discount %}}{100}\right) \]

Step 3: Detailed Explanation:
1. Let us assume the Cost Price of the article is \(CP = 100x\).
2. According to the question, the shopkeeper marks the article 40% above its cost price.
Therefore, the Marked Price (\(MP\)) is:
\[ MP = 100x + 40% \text{ of } 100x = 140x \].
3. Next, the shopkeeper allows a discount of 10% on this marked price.
The discount amount is calculated on the Marked Price:
\[ \text{Discount} = 10% \text{ of } 140x = 14x \].
4. The Selling Price (\(SP\)) is the Marked Price minus the discount:
\[ SP = MP - \text{Discount} = 140x - 14x = 126x \].
5. The actual selling price of the article is given as Rs 1,260.
We can now equate our algebraic representation of the Selling Price to the actual value:
\[ 126x = 1260 \].
6. Solving for \(x\), we get:
\[ x = \frac{1260}{126} = 10 \].
7. Now, we substitute the value of \(x\) back into our assumption for the Cost Price:
\[ CP = 100x = 100 \times 10 = 1000 \].

Step 4: Final Answer:
Therefore, the cost price of the article is Rs 1,000, which corresponds to Option (A).