A camera is sold for ₹ 4600. If it was sold at a profit of 15%, what was its CP?

Options

A. ₹ 4500
B. ₹ 3500
C. ₹ 4000
D. ₹ 4200

Answer

To find the cost price (CP) of the camera when it is sold for ₹4600 at a profit of 15%, we can follow these steps:

### Step 1: Understand the relationship between Selling Price (SP), Cost Price (CP), and Profit
The relationship can be expressed as:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where:
- SP = Selling Price
- CP = Cost Price
- Profit = (Profit Percentage × CP) / 100

### Step 2: Set up the equation
Given that the Selling Price (SP) is ₹4600 and the profit percentage is 15%, we can express the profit in terms of CP:
\[ \text{Profit} = \frac{15}{100} \times \text{CP} \]

### Step 3: Substitute the profit into the SP equation
Substituting the profit into the SP equation gives us:
\[ 4600 = \text{CP} + \frac{15}{100} \times \text{CP} \]

### Step 4: Combine like terms
We can factor out CP from the right side:
\[ 4600 = \text{CP} \left(1 + \frac{15}{100}\right) \]
\[ 4600 = \text{CP} \left(\frac{100 + 15}{100}\right) \]
\[ 4600 = \text{CP} \left(\frac{115}{100}\right) \]

### Step 5: Solve for CP
To find CP, we rearrange the equation:
\[ \text{CP} = \frac{4600 \times 100}{115} \]

### Step 6: Calculate CP
Now, we can perform the calculation:
\[ \text{CP} = \frac{460000}{115} \]
\[ \text{CP} = 4000 \]

### Conclusion
The cost price of the camera is ₹4000.