Cost price of article A is Rs 600 more than that of B and selling price of A is Rs 1200 more than that of B. If difference between profit earned on selling these two articles is `13(1)/(3)`% of the cost price of A then find profit earned on B if profit % earned on A is `33(1)/(3)`%?

Options

A. A)Rs 800
B. B)Rs 900
C. C)Rs 840
D. D)Rs 960

Answer

To solve the problem step by step, we will follow the information provided in the question.

### Step 1: Define the Cost Prices
Let the cost price of article B be \( CP_B \).
According to the question, the cost price of article A is Rs 600 more than that of B. Therefore, we can express the cost price of article A as:
\[ CP_A = CP_B + 600 \]

### Step 2: Express Selling Prices
The selling price of article A is Rs 1200 more than that of B. Let the selling price of article B be \( SP_B \). Thus, we can express the selling price of article A as:
\[ SP_A = SP_B + 1200 \]

### Step 3: Profit Percentages
It is given that the profit percentage on article A is \( 33\frac{1}{3}\% \). This can be expressed as a fraction:
\[ \text{Profit Percentage on A} = \frac{1}{3} \]
The profit on article A can be calculated as:
\[ \text{Profit on A} = SP_A - CP_A \]
Using the profit percentage:
\[ \frac{SP_A - CP_A}{CP_A} = \frac{1}{3} \]
This implies:
\[ SP_A - CP_A = \frac{1}{3} CP_A \]
Thus,
\[ SP_A = CP_A + \frac{1}{3} CP_A = \frac{4}{3} CP_A \]

### Step 4: Substitute the Cost Price of A
Substituting \( CP_A \) from Step 1 into the equation:
\[ SP_A = \frac{4}{3}(CP_B + 600) \]

### Step 5: Calculate Selling Price of B
From Step 2, we have:
\[ SP_A = SP_B + 1200 \]
Substituting \( SP_A \):
\[ \frac{4}{3}(CP_B + 600) = SP_B + 1200 \]

### Step 6: Express Selling Price of B in Terms of CP_B
Now we can express \( SP_B \):
\[ SP_B = \frac{4}{3}(CP_B + 600) - 1200 \]

### Step 7: Calculate Profit on B
The profit on article B is given by:
\[ \text{Profit on B} = SP_B - CP_B \]
Substituting \( SP_B \):
\[ \text{Profit on B} = \left(\frac{4}{3}(CP_B + 600) - 1200\right) - CP_B \]

### Step 8: Simplify the Profit on B
Now, we simplify the profit on B:
\[ \text{Profit on B} = \frac{4}{3}CP_B + 800 - 1200 - CP_B \]
\[ = \frac{4}{3}CP_B - CP_B - 400 \]
\[ = \frac{4}{3}CP_B - \frac{3}{3}CP_B - 400 \]
\[ = \frac{1}{3}CP_B - 400 \]

### Step 9: Find the Difference in Profits
The difference in profits between articles A and B is given as \( 13\frac{1}{3}\% \) of the cost price of A. This can be expressed as:
\[ \text{Difference} = \frac{4}{30} \times CP_A \]
Substituting \( CP_A \):
\[ \frac{4}{30} \times (CP_B + 600) \]

### Step 10: Set Up the Equation
Setting the difference in profits equal to the calculated difference:
\[ \left( \frac{1}{3}CP_B - 400 \right) - 100 = \frac{4}{30}(CP_B + 600) \]

### Step 11: Solve for CP_B
Solving this equation will give us the value of \( CP_B \), and subsequently, we can find the profit on B.

### Step 12: Calculate the Profit on B
Finally, substituting the value of \( CP_B \) back into the profit formula for B will yield the profit earned on B.