The difference between the selling prices of a chair at profits 10% and 14% is Rs 27. What is the cost price of the chair?
A)Rs 586
B)Rs 440
C)Rs 880
D)Rs 675

Options

A. Rs 586
B. Rs 440
C. Rs 880
D. Rs 675

Answer

To solve the problem, we need to find the cost price of a chair given that the difference between the selling prices at a profit of 10% and 14% is Rs 27.

### Step-by-Step Solution:

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

2. **Calculate Selling Prices**:
- Selling Price at 10% profit:
\[ SP_{10} = CP + 10\% \text{ of } CP = CP + 0.10 \times CP = 1.10 \times CP \]
- Selling Price at 14% profit:
\[ SP_{14} = CP + 14\% \text{ of } CP = CP + 0.14 \times CP = 1.14 \times CP \]

3. **Find the Difference in Selling Prices**:
According to the problem, the difference between the two selling prices is Rs 27:
\[ SP_{14} - SP_{10} = 27 \]
Substituting the expressions for \( SP_{10} \) and \( SP_{14} \):
\[ (1.14 \times CP) - (1.10 \times CP) = 27 \]

4. **Simplify the Equation**:
\[ (1.14 - 1.10) \times CP = 27 \]
\[ 0.04 \times CP = 27 \]

5. **Solve for Cost Price (CP)**:
\[ CP = \frac{27}{0.04} \]
\[ CP = 675 \]

Thus, the cost price of the chair is **Rs 675**.

### Final Answer:
The cost price of the chair is **Rs 675** (Option D).