A trader marks an article 25% above its cost price. He allows a discount of 10% on the marked price. After giving the discount, he makes a profit of ₹180 on the article. What is the cost price of the article?
₹1,440
To solve the problem, we need to determine the cost price (CP) of the article using the given information about the marked price (MP), discount, and profit. Let's break down the solution step-by-step:
- The article is marked 25% above its cost price. Therefore, the marked price (MP) can be expressed in terms of the cost price (CP) as follows:
\(MP = CP + 0.25 \times CP = 1.25 \times CP\)
- The trader offers a discount of 10% on the marked price. Thus, the selling price (SP) after the discount can be calculated as:
\(SP = MP - 0.10 \times MP = 0.90 \times MP\)
- Substitute the expression for MP from step 1 into the equation for SP:
\(SP = 0.90 \times (1.25 \times CP) = 1.125 \times CP\)
- According to the problem statement, the trader makes a profit of ₹180 on the article. Since profit is defined as the difference between the selling price and the cost price, we have:
\(SP - CP = 180\)
- Substitute the expression for SP from step 3:
\(1.125 \times CP - CP = 180\)
- Simplify this equation:
\(0.125 \times CP = 180\)
- Solve for CP:
\(CP = \frac{180}{0.125} = 1440\)
Therefore, the cost price of the article is ₹1,440.
This value corresponds to the correct answer option: ₹1,440.
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