The cost price of 60 articles is same as the selling price of x articles. If there is a profit of 20% what is the value of x?

Options

A. 15
B. 30
C. 50
D. 80

Answer

To solve the problem, we need to find the value of \( x \) given that the cost price of 60 articles is the same as the selling price of \( x \) articles, and there is a profit of 20%.

### Step-by-step Solution:

1. **Define the Cost Price (CP)**:
Let's assume the cost price of 1 article is Rs 1. Therefore, the cost price of 60 articles will be:
\[ \text{CP of 60 articles} = 60 \times 1 = Rs 60 \]

2. **Calculate Selling Price (SP)**:
Since there is a profit of 20%, we can calculate the selling price of 1 article. The formula for selling price when profit percentage is given is:
\[ \text{SP} = \text{CP} + \text{Profit} \]
The profit can be calculated as:
\[ \text{Profit} = \frac{20}{100} \times \text{CP} = 0.2 \times 1 = Rs 0.2 \]
Therefore, the selling price of 1 article is:
\[ \text{SP of 1 article} = 1 + 0.2 = Rs 1.2 \]

3. **Selling Price of \( x \) Articles**:
The selling price of \( x \) articles will be:
\[ \text{SP of } x \text{ articles} = x \times \text{SP of 1 article} = x \times 1.2 \]

4. **Set the Selling Price Equal to Cost Price**:
According to the problem, the cost price of 60 articles is equal to the selling price of \( x \) articles:
\[ 60 = x \times 1.2 \]

5. **Solve for \( x \)**:
To find \( x \), we can rearrange the equation:
\[ x = \frac{60}{1.2} \]
Now, calculate \( x \):
\[ x = 60 \div 1.2 = 50 \]

Thus, the value of \( x \) is \( 50 \).

### Final Answer:
\[ \text{The value of } x \text{ is } 50. \]