Ramu bought two items A and B. The cost price of Item B was `12%` more than that of Item A. Ramu sold each of the items at `25%` profit. If the difference between the profits earned from both the items was ₹6,what was the cost price (in ₹) of Item A?

Options

A. 360
B. 240
C. 250
D. 200

Answer

To solve the problem step by step, we will denote the cost price of Item A as \( CP_A \) and the cost price of Item B as \( CP_B \).

### Step 1: Define the cost price of Item A
Let the cost price of Item A be \( CP_A = 100x \).

### Step 2: Calculate the cost price of Item B
Since the cost price of Item B is 12% more than that of Item A, we can express it as:
\[ CP_B = CP_A + 12\% \text{ of } CP_A = 100x + 0.12 \times 100x = 112x \]

### Step 3: Calculate the selling price of both items
Ramu sells each item at a profit of 25%. Therefore, the selling price of Item A and Item B can be calculated as follows:
\[ \text{Selling Price of Item A} = CP_A + 25\% \text{ of } CP_A = 100x + 0.25 \times 100x = 125x \]
\[ \text{Selling Price of Item B} = CP_B + 25\% \text{ of } CP_B = 112x + 0.25 \times 112x = 140x \]

### Step 4: Calculate the profit from both items
The profit earned from each item can be calculated as:
\[ \text{Profit from Item A} = \text{Selling Price of Item A} - CP_A = 125x - 100x = 25x \]
\[ \text{Profit from Item B} = \text{Selling Price of Item B} - CP_B = 140x - 112x = 28x \]

### Step 5: Set up the equation based on the difference in profits
According to the problem, the difference between the profits earned from both items is ₹6:
\[ \text{Profit from Item B} - \text{Profit from Item A} = 6 \]
Substituting the profit values we calculated:
\[ 28x - 25x = 6 \]
This simplifies to:
\[ 3x = 6 \]

### Step 6: Solve for x
Dividing both sides by 3 gives:
\[ x = 2 \]

### Step 7: Calculate the cost price of Item A
Now that we have the value of \( x \), we can find the cost price of Item A:
\[ CP_A = 100x = 100 \times 2 = 200 \]

### Final Answer
The cost price of Item A is ₹200.

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