On selling an article for Rs. 1470 a man gets profit of 22.5%. Find the cost price of the aricle.

Answer

To find the cost price of the article when it is sold for Rs. 1470 with a profit of 22.5%, we can follow these steps:

### Step 1: Understand the relationship between Selling Price, Cost Price, and Profit
The relationship can be expressed as:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]
Where Profit can be calculated as a percentage of the Cost Price.

### Step 2: Express Profit in terms of Cost Price
Given that the profit is 22.5%, we can express it as:
\[ \text{Profit} = \frac{22.5}{100} \times \text{CP} \]
This can also be written as:
\[ \text{Profit} = 0.225 \times \text{CP} \]

### Step 3: Substitute Profit in the Selling Price equation
Substituting the expression for Profit into the Selling Price equation gives:
\[ \text{SP} = \text{CP} + 0.225 \times \text{CP} \]
This simplifies to:
\[ \text{SP} = \text{CP} (1 + 0.225) = \text{CP} \times 1.225 \]

### Step 4: Rearrange to find Cost Price
Now, we can rearrange this equation to solve for Cost Price (CP):
\[ \text{CP} = \frac{\text{SP}}{1.225} \]

### Step 5: Substitute the Selling Price
We know the Selling Price (SP) is Rs. 1470, so we substitute this value into the equation:
\[ \text{CP} = \frac{1470}{1.225} \]

### Step 6: Calculate the Cost Price
Now, we perform the division:
\[ \text{CP} = \frac{1470}{1.225} \approx 1200 \]

Thus, the cost price of the article is Rs. 1200.

### Summary
The cost price of the article is Rs. 1200.

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