If by selling an article for Rs. 390 a shopkeeper gains 20%, then the cost price is

Options

A. Rs.370
B. Rs.325
C. Rs.350
D. Rs.300

Answer

To find the cost price of the article, we can follow these steps:

### Step 1: Understand the relationship between Selling Price (SP), Cost Price (CP), and Profit Percentage
We know that:
- Selling Price (SP) = Cost Price (CP) + Profit
- Profit = (Profit Percentage / 100) × Cost Price

### Step 2: Define the variables
Let the Cost Price (CP) be denoted as \( X \).

### Step 3: Calculate the Profit
Given that the profit percentage is 20%, we can express the profit as:
\[ \text{Profit} = \frac{20}{100} \times X = \frac{X}{5} \]

### Step 4: Write the equation for Selling Price
The Selling Price (SP) can be expressed as:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Substituting the values we have:
\[ 390 = X + \frac{X}{5} \]

### Step 5: Combine the terms
To combine the terms on the right side, we can express \( X \) as a fraction:
\[ 390 = \frac{5X}{5} + \frac{X}{5} \]
\[ 390 = \frac{6X}{5} \]

### Step 6: Solve for X
To isolate \( X \), multiply both sides by 5:
\[ 390 \times 5 = 6X \]
\[ 1950 = 6X \]
Now, divide both sides by 6:
\[ X = \frac{1950}{6} \]
\[ X = 325 \]

### Conclusion
The Cost Price (CP) of the article is Rs. 325.

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