By selling an articles for Rs 3375 a person loses 10%. Find his profit per cent, if he sell it for Rs 4500.

Options

A. 18
B. 24
C. 28
D. None of these

Answer

To solve the problem step by step, we need to find the cost price (CP) of the article first and then calculate the profit percentage when the selling price (SP) is Rs 4500.

### Step 1: Determine the Cost Price (CP)
Given:
- Selling Price (SP) = Rs 3375
- Loss Percentage = 10%

Using the formula for loss:
\[ \text{Loss} = \text{CP} - \text{SP} \]
We can also express the loss in terms of CP:
\[ \text{Loss} = \frac{\text{Loss Percentage}}{100} \times \text{CP} \]
Substituting the values:
\[ \frac{10}{100} \times \text{CP} = \text{CP} - 3375 \]
This simplifies to:
\[ 0.1 \times \text{CP} = \text{CP} - 3375 \]
Rearranging gives:
\[ \text{CP} - 0.1 \times \text{CP} = 3375 \]
\[ 0.9 \times \text{CP} = 3375 \]
Now, solving for CP:
\[ \text{CP} = \frac{3375}{0.9} = 3750 \]

### Step 2: Calculate the Profit when Selling Price is Rs 4500
Now, we know:
- Cost Price (CP) = Rs 3750
- New Selling Price (SP) = Rs 4500

The profit can be calculated as:
\[ \text{Profit} = \text{SP} - \text{CP} = 4500 - 3750 = 750 \]

### Step 3: Calculate the Profit Percentage
To find the profit percentage, we use the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left(\frac{750}{3750}\right) \times 100 \]
Calculating this gives:
\[ \text{Profit Percentage} = \left(\frac{1}{5}\right) \times 100 = 20\% \]

### Final Answer
The profit percentage when the article is sold for Rs 4500 is **20%**.

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