The cost price of an article A is 20% more than that of B, A is sold for Rs 1,800 at a loss of 20% and B is sold such that there is a profit of 20% on both A and B together. The selling price of B is :

Options

A. Rs 3,150
B. Rs 2,980
C. Rs 3,120
D. Rs 2,940

Answer

To solve the problem step by step, let's break down the information given and calculate the selling price of article B.

### Step 1: Define the Cost Prices
Let the cost price of article B be \( CP_B = x \).
Since the cost price of article A is 20% more than that of B, we can express the cost price of article A as:
\[ CP_A = CP_B + 20\% \text{ of } CP_B = x + 0.2x = 1.2x \]

### Step 2: Calculate the Cost Price of A
Article A is sold for Rs 1,800 at a loss of 20%. The selling price (SP) is related to the cost price (CP) by the formula:
\[ SP = CP - \text{Loss} \]
Given that the loss is 20%, we can express this as:
\[ SP_A = CP_A \times (1 - 0.2) = CP_A \times 0.8 \]
Substituting the selling price:
\[ 1800 = CP_A \times 0.8 \]
Now, solving for \( CP_A \):
\[ CP_A = \frac{1800}{0.8} = 2250 \]

### Step 3: Calculate the Cost Price of B
Now that we know \( CP_A \), we can find \( CP_B \):
\[ CP_A = 1.2x \implies 2250 = 1.2x \]
Solving for \( x \):
\[ x = \frac{2250}{1.2} = 1875 \]
Thus, \( CP_B = 1875 \).

### Step 4: Calculate Total Cost Price
Now we can find the total cost price of both articles A and B:
\[ \text{Total CP} = CP_A + CP_B = 2250 + 1875 = 4125 \]

### Step 5: Calculate Total Selling Price for Profit
The problem states that there is a profit of 20% on both A and B together. Therefore, the total selling price can be calculated as:
\[ \text{Total SP} = \text{Total CP} \times (1 + \text{Profit Percentage}) = 4125 \times (1 + 0.2) = 4125 \times 1.2 = 4950 \]

### Step 6: Calculate Selling Price of B
We know the selling price of A is Rs 1,800. To find the selling price of B, we can use:
\[ \text{Total SP} = SP_A + SP_B \]
Thus,
\[ 4950 = 1800 + SP_B \]
Solving for \( SP_B \):
\[ SP_B = 4950 - 1800 = 3150 \]

### Final Answer
The selling price of article B is Rs 3,150.

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