The cost price of 19 articles is same as the selling price of 29 articles. What is the loss `%`?

Options

A. `35%`
B. `34.48%`
C. `52.63%`
D. none of these

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Define the Cost Price (CP) and Selling Price (SP)
Let the cost price of one article be \( x \). Therefore, the cost price of 19 articles will be:
\[ \text{CP of 19 articles} = 19x \]

Let the selling price of one article be \( y \). Therefore, the selling price of 29 articles will be:
\[ \text{SP of 29 articles} = 29y \]

### Step 2: Set Up the Equation
According to the problem, the cost price of 19 articles is equal to the selling price of 29 articles:
\[ 19x = 29y \]

### Step 3: Find the Ratio of CP to SP
We can rearrange the equation to find the ratio of \( x \) to \( y \):
\[ \frac{x}{y} = \frac{29}{19} \]

### Step 4: Calculate the Loss
To find the loss, we first need to determine how much we lose per article. The loss per article can be calculated as:
\[ \text{Loss} = \text{CP} - \text{SP} = x - y \]

Using the ratio we found earlier, we can express \( y \) in terms of \( x \):
\[ y = \frac{19}{29}x \]
Now substituting this into the loss formula:
\[ \text{Loss} = x - \frac{19}{29}x = x\left(1 - \frac{19}{29}\right) = x\left(\frac{29 - 19}{29}\right) = x\left(\frac{10}{29}\right) \]

### Step 5: Calculate the Loss Percentage
The loss percentage is given by:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{CP}}\right) \times 100 \]
Substituting the values we have:
\[ \text{Loss Percentage} = \left(\frac{x \left(\frac{10}{29}\right)}{x}\right) \times 100 = \left(\frac{10}{29}\right) \times 100 \]
Calculating this gives:
\[ \text{Loss Percentage} = \frac{1000}{29} \approx 34.48\% \]

### Final Answer
The loss percentage is approximately \( 34.48\% \).

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