A dealer gets `Rs.56` less if instead of selling a chair at a gain of `15%`, its it is sold at a gain of `8%`.
Find the cost price of the chair.

Options

A. `Rs.500`
B. `Rs.600`
C. `Rs.700`
D. `Rs.800`

Answer

To solve the problem step by step, we will first define the variables and then set up the equations based on the information provided.

### Step 1: Define the Cost Price
Let the cost price of the chair be \( X \).

### Step 2: Calculate Selling Price at 15% Gain
The selling price (SP) when sold at a gain of 15% can be calculated using the formula:
\[ \text{SP} = \text{CP} + \text{Gain} \]
Where Gain = \( \frac{15}{100} \times X \).

Thus, the selling price at 15% gain is:
\[ \text{SP}_{15\%} = X + \frac{15}{100} \times X = \frac{115}{100} \times X = 1.15X \]

### Step 3: Calculate Selling Price at 8% Gain
Similarly, the selling price when sold at a gain of 8% is:
\[ \text{SP}_{8\%} = X + \frac{8}{100} \times X = \frac{108}{100} \times X = 1.08X \]

### Step 4: Set Up the Equation
According to the problem, the dealer gets Rs. 56 less when selling at 8% gain compared to selling at 15% gain. Therefore, we can set up the equation:
\[ \text{SP}_{15\%} - \text{SP}_{8\%} = 56 \]
Substituting the expressions we found:
\[ 1.15X - 1.08X = 56 \]

### Step 5: Simplify the Equation
Now, simplify the left side:
\[ (1.15 - 1.08)X = 56 \]
\[ 0.07X = 56 \]

### Step 6: Solve for X
To find \( X \), divide both sides by 0.07:
\[ X = \frac{56}{0.07} \]
Calculating this gives:
\[ X = 800 \]

### Conclusion
The cost price of the chair is Rs. 800.

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