A shopkeepr allows 28% discount on the marked price of an article and still makes a profit of 20% If be gians Rs.30.80 on the sale of one article. Then what will be the cost price of the article ?

Options

A. Rs 145
B. Rs. 160
C. Rs. 164
D. Rs. 154

Answer

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

### Step-by-Step Solution:

1. **Define the Variables**:
Let the cost price of the article be \( x \).

2. **Calculate the Selling Price**:
Since the shopkeeper makes a profit of 20%, the selling price (SP) can be calculated as:
\[ SP = CP + \text{Profit} = x + 0.2x = 1.2x \]

3. **Determine the Gain**:
The gain is given as Rs. 30.80. The gain can also be expressed as:
\[ \text{Gain} = SP - CP = 1.2x - x = 0.2x \]

4. **Set Up the Equation**:
We know from the problem that the gain is Rs. 30.80, so we can set up the equation:
\[ 0.2x = 30.80 \]

5. **Solve for \( x \)**:
To find \( x \), we can rearrange the equation:
\[ x = \frac{30.80}{0.2} \]
Now, calculate \( x \):
\[ x = 30.80 \div 0.2 = 154 \]

6. **Conclusion**:
Therefore, the cost price of the article is Rs. 154.

### Final Answer:
The cost price of the article is Rs. 154.