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

Options

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

Answer

To find the cost price (CP) of the camera when it is sold for Rs. 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 Percentage
The formula to calculate Selling Price when you know the Cost Price and Profit Percentage is:
\[ SP = CP + \text{Profit} \]
Where Profit can be calculated as:
\[ \text{Profit} = \left( \frac{\text{Profit Percentage}}{100} \times CP \right) \]

### Step 2: Rewrite the Selling Price formula in terms of CP
Since we know that:
\[ SP = CP + \left( \frac{15}{100} \times CP \right) \]
This can be simplified to:
\[ SP = CP \left(1 + \frac{15}{100}\right) \]
\[ SP = CP \left(\frac{100 + 15}{100}\right) \]
\[ SP = CP \left(\frac{115}{100}\right) \]

### Step 3: Substitute the known Selling Price
We know that the Selling Price (SP) is Rs. 4600. So we can write:
\[ 4600 = CP \left(\frac{115}{100}\right) \]

### Step 4: Solve for Cost Price (CP)
To find CP, we rearrange the equation:
\[ CP = 4600 \times \left(\frac{100}{115}\right) \]
Now, calculate:
\[ CP = 4600 \times \frac{100}{115} \]
\[ CP = 4600 \times \frac{20}{23} \]
\[ CP = \frac{92000}{23} \]
Calculating this gives:
\[ CP \approx 4000 \]

### Final Answer
The Cost Price (CP) of the camera is Rs. 4000.

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