The marked price of an article is ₹400. A shopkeeper sells it by giving two successive discounts of 12% and 20% on its marked price. If he earns a profit of 10%, then the cost price of the article is:

Options

A. ₹250
B. ₹260
C. ₹256
D. ₹268

Answer

To find the cost price of the article given the marked price and successive discounts, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Marked Price (MP)**:
The marked price of the article is given as ₹400.

2. **Calculate the Successive Discounts**:
The shopkeeper gives two successive discounts of 12% and 20%. We can use the formula for successive discounts:
\[ \text{Effective Discount} = A + B - \frac{A \times B}{100} \]
where \( A = 12 \) and \( B = 20 \).

Substituting the values:
\[ \text{Effective Discount} = 12 + 20 - \frac{12 \times 20}{100} \]
\[ = 32 - \frac{240}{100} \]
\[ = 32 - 2.4 = 29.6\% \]

3. **Calculate the Selling Price (SP)**:
The selling price can be calculated using the effective discount:
\[ \text{Selling Price} = \text{Marked Price} - \text{Discount} \]
First, calculate the discount amount:
\[ \text{Discount Amount} = \frac{29.6}{100} \times 400 = 118.4 \]
Now, calculate the selling price:
\[ \text{Selling Price} = 400 - 118.4 = 281.6 \]

4. **Determine the Cost Price (CP)**:
We know that the shopkeeper earns a profit of 10%. The selling price is related to the cost price by the formula:
\[ \text{Selling Price} = \text{Cost Price} + \text{Profit} \]
Since profit is 10% of the cost price, we can express this as:
\[ \text{Selling Price} = \text{Cost Price} + 0.10 \times \text{Cost Price} = 1.10 \times \text{Cost Price} \]
Rearranging gives:
\[ \text{Cost Price} = \frac{\text{Selling Price}}{1.10} \]
Substituting the selling price:
\[ \text{Cost Price} = \frac{281.6}{1.10} = 256 \]

### Final Answer:
The cost price of the article is ₹256.

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