To solve this problem, let's denote the cost price of the article as [tex]\( Cp \)[/tex].
### Step 1: Calculate the Selling Price at 22% Profit
First, we need to understand what it means to sell the article at a 22% profit.
The selling price (SP1) in this case can be calculated as:
[tex]\[ SP1 = Cp \times (1 + \frac{22}{100}) \][/tex]
[tex]\[ SP1 = Cp \times 1.22 \][/tex]
### Step 2: Calculate the Selling Price at 25% Profit with a 12% Reduced Cost Price
Next, if the shopkeeper buys the article at a price 12% less than the original cost price and sells it at a 25% profit, we have:
The reduced cost price (RCP) is:
[tex]\[ RCP = Cp \times (1 - \frac{12}{100}) \][/tex]
[tex]\[ RCP = Cp \times 0.88 \][/tex]
The new selling price (SP2) at a 25% profit would be:
[tex]\[ SP2 = RCP \times (1 + \frac{25}{100}) \][/tex]
[tex]\[ SP2 = Cp \times 0.88 \times 1.25 \][/tex]
[tex]\[ SP2 = Cp \times 1.10 \][/tex]
### Step 3: Given the Difference in Profits
According to the problem, the difference in the profit is Rs. 66 when comparing these two scenarios:
[tex]\[ SP1 - SP2 = 66 \][/tex]
Substituting the SP values:
[tex]\[ Cp \times 1.22 - Cp \times 1.10 = 66 \][/tex]
### Step 4: Solve for Cost Price (Cp)
Let's simplify and solve this equation:
[tex]\[ Cp \times 1.22 - Cp \times 1.10 = 66 \][/tex]
[tex]\[ Cp \times (1.22 - 1.10) = 66 \][/tex]
[tex]\[ Cp \times 0.12 = 66 \][/tex]
[tex]\[ Cp = \frac{66}{0.12} \][/tex]
[tex]\[ Cp = 550 \][/tex]
Therefore, the cost price of the article is [tex]\( \text{Rs. 550} \)[/tex].
So, the correct answer is:
(B) Rs. 550
