The difference between the selling prices of an article at a prof It of 15% and at a profit of 10% Is 10. The cost price of the article is

Options

A. 100
B. 120
C. 150
D. 200

Answer

To solve the problem, we need to find the cost price (CP) of the article given that the difference between the selling prices (SP) at a profit of 15% and a profit of 10% is 10.

### Step-by-Step Solution:

1. **Define the Cost Price (CP)**:
Let the cost price of the article be \( CP \).

2. **Calculate Selling Price at 15% Profit**:
The selling price at a profit of 15% can be calculated as:
\[ SP_{15} = CP + 15\% \text{ of } CP = CP + 0.15 \times CP = 1.15 \times CP \]

3. **Calculate Selling Price at 10% Profit**:
The selling price at a profit of 10% can be calculated as:
\[ SP_{10} = CP + 10\% \text{ of } CP = CP + 0.10 \times CP = 1.10 \times CP \]

4. **Set Up the Equation**:
According to the problem, the difference between the selling prices at 15% and 10% profit is 10:
\[ SP_{15} - SP_{10} = 10 \]
Substituting the expressions for \( SP_{15} \) and \( SP_{10} \):
\[ (1.15 \times CP) - (1.10 \times CP) = 10 \]

5. **Simplify the Equation**:
\[ 1.15CP - 1.10CP = 10 \]
\[ 0.05CP = 10 \]

6. **Solve for Cost Price (CP)**:
To find \( CP \), divide both sides by 0.05:
\[ CP = \frac{10}{0.05} = 200 \]

### Final Answer:
The cost price of the article is \( \text{Rs. } 200 \).

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