A dealer gets Rs. 30 less if instead of selling a chair at a gain of 12% he sells it at a gain of 8%. Find the cost price of the chair?

Answer

To solve the problem, we need to find the cost price (CP) of the chair based on the information given about the selling prices at different profit percentages. Let's break it down step by step.

### Step 1: Define the Variables
Let the cost price of the chair be \( CP \).

### Step 2: Calculate Selling Prices
1. **Selling Price at 12% Gain**:
\[ SP_{12\%} = CP + 12\% \text{ of } CP = CP + \frac{12}{100} \times CP = CP \times \left(1 + \frac{12}{100}\right) = CP \times 1.12 \]

2. **Selling Price at 8% Gain**:
\[ SP_{8\%} = CP + 8\% \text{ of } CP = CP + \frac{8}{100} \times CP = CP \times \left(1 + \frac{8}{100}\right) = CP \times 1.08 \]

### Step 3: Set Up the Equation
According to the problem, the dealer gets Rs. 30 less when selling at an 8% gain compared to selling at a 12% gain. Therefore, we can set up the equation:
\[ SP_{12\%} - SP_{8\%} = 30 \]
Substituting the expressions we found for the selling prices:
\[ CP \times 1.12 - CP \times 1.08 = 30 \]

### Step 4: Simplify the Equation
Factor out \( CP \):
\[ CP \times (1.12 - 1.08) = 30 \]
\[ CP \times 0.04 = 30 \]

### Step 5: Solve for Cost Price
Now, divide both sides by 0.04 to find \( CP \):
\[ CP = \frac{30}{0.04} = 750 \]

### Conclusion
The cost price of the chair is Rs. 750.

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