The cost price of 30 articles is the same as the selling price of 24 articles. If the profit is x%, then the value of x is:

Options

A. 18
B. 30
C. 25
D. 24

Answer

To solve the problem step-by-step, we will follow the logical deductions made in the video transcript.

### Step 1: Understand the relationship between Cost Price (CP) and Selling Price (SP)
The problem states that the cost price of 30 articles is equal to the selling price of 24 articles. We can express this relationship mathematically:

\[ \text{Cost Price of 30 articles} = \text{Selling Price of 24 articles} \]

Let the cost price of one article be \( CP \) and the selling price of one article be \( SP \). Therefore, we can write:

\[ 30 \times CP = 24 \times SP \]

### Step 2: Rearranging the equation
We can rearrange the equation to find the ratio of SP to CP:

\[ \frac{SP}{CP} = \frac{30}{24} \]

### Step 3: Simplifying the ratio
Now, we simplify the fraction:

\[ \frac{30}{24} = \frac{5}{4} \]

So, we have:

\[ \frac{SP}{CP} = \frac{5}{4} \]

### Step 4: Understanding profit percentage
The profit percentage \( x \) is defined as:

\[ \text{Profit Percentage} = \frac{SP - CP}{CP} \times 100 \]

### Step 5: Substitute the ratio into the profit percentage formula
From our earlier result, we know:

\[ \frac{SP}{CP} = \frac{5}{4} \]

We can express \( SP \) in terms of \( CP \):

\[ SP = \frac{5}{4} \times CP \]

Now, substituting this into the profit percentage formula:

\[ \text{Profit Percentage} = \frac{\left(\frac{5}{4} \times CP - CP\right)}{CP} \times 100 \]

### Step 6: Simplifying the profit calculation
Now, simplify the expression inside the brackets:

\[ \frac{5}{4} \times CP - CP = \left(\frac{5}{4} - 1\right) \times CP = \left(\frac{5}{4} - \frac{4}{4}\right) \times CP = \frac{1}{4} \times CP \]

Now substitute this back into the profit percentage formula:

\[ \text{Profit Percentage} = \frac{\frac{1}{4} \times CP}{CP} \times 100 = \frac{1}{4} \times 100 = 25\% \]

### Step 7: Conclusion
Thus, the value of \( x \) is:

\[ x = 25 \]

### Final Answer
The value of \( x \) is **25**.

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