If a shopkeeper sells an article for Rs. 420 and makes a profit of 20%, find its cost price.

Answer

To find the cost price of an article sold for Rs. 420 with a profit of 20%, we can follow these steps:

### Step 1: Understand the given information
- Selling Price (SP) = Rs. 420
- Profit Percentage = 20%

### Step 2: Set up the formula for Profit Percentage
The formula for profit percentage is given by:
\[ \text{Profit Percentage} = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100 \]
Let the Cost Price (CP) be \( x \).

### Step 3: Substitute the known values into the formula
Substituting the values we have:
\[ 20 = \frac{420 - x}{x} \times 100 \]

### Step 4: Simplify the equation
First, divide both sides by 100:
\[ 0.2 = \frac{420 - x}{x} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives:
\[ 0.2x = 420 - x \]

### Step 6: Rearrange the equation
Rearranging the equation, we get:
\[ 0.2x + x = 420 \]
This simplifies to:
\[ 1.2x = 420 \]

### Step 7: Solve for x (Cost Price)
Now, divide both sides by 1.2 to find \( x \):
\[ x = \frac{420}{1.2} \]

### Step 8: Calculate the Cost Price
Calculating the right side:
\[ x = 350 \]

### Conclusion
Thus, the Cost Price (CP) of the article is Rs. 350.

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