A shopkeeper sold 12 cameras at the profit of 20% and 8 cameras profit of 10%. If he had sold all 20 cameras at 15% profit then his profit would have been decreased by Rs. 36. What is the cost price of each camera?

Answer

To solve the problem step by step, let's define the variables and calculate the cost price of each camera.

### Step 1: Define the Cost Price
Let the cost price (CP) of each camera be \( x \).

### Step 2: Calculate Selling Price for 12 Cameras at 20% Profit
The selling price (SP) for 12 cameras sold at a profit of 20% can be calculated as follows:
\[ \text{SP for 12 cameras} = 12 \times (x + 0.2x) = 12 \times 1.2x = 14.4x \]

### Step 3: Calculate Selling Price for 8 Cameras at 10% Profit
The selling price for 8 cameras sold at a profit of 10% can be calculated as follows:
\[ \text{SP for 8 cameras} = 8 \times (x + 0.1x) = 8 \times 1.1x = 8.8x \]

### Step 4: Calculate Total Selling Price for 20 Cameras
The total selling price when 12 cameras are sold at 20% profit and 8 cameras at 10% profit is:
\[ \text{Total SP} = 14.4x + 8.8x = 23.2x \]

### Step 5: Calculate Selling Price if All 20 Cameras Sold at 15% Profit
If all 20 cameras are sold at a profit of 15%, the selling price would be:
\[ \text{SP for 20 cameras at 15%} = 20 \times (x + 0.15x) = 20 \times 1.15x = 23x \]

### Step 6: Set Up the Equation Based on the Given Condition
According to the problem, the profit would decrease by Rs. 36 if all cameras were sold at 15% profit. Therefore, we can set up the equation:
\[ 23.2x - 23x = 36 \]
\[ 0.2x = 36 \]

### Step 7: Solve for x
Now, solve for \( x \):
\[ x = \frac{36}{0.2} = 180 \]

### Conclusion
The cost price of each camera is Rs. 180.

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