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

Options

A. 0.35
B. 0.3448
C. 0.5263
D. none of these

Answer

To solve the problem step by step, we will follow the information given and apply the relevant formulas.

### Step 1: Understand the relationship between Cost Price (CP) and Selling Price (SP)
We know from the problem that the cost price of 19 articles is equal to the selling price of 29 articles. This means:
- Let the cost price of one article be \( CP \).
- Let the selling price of one article be \( SP \).

From the information given:
\[ 19 \times CP = 29 \times SP \]

### Step 2: Express SP in terms of CP
Rearranging the equation gives us:
\[ SP = \frac{19}{29} \times CP \]

### Step 3: Determine the loss
Loss occurs when the cost price is greater than the selling price. The loss can be calculated as:
\[ \text{Loss} = CP - SP \]

Substituting the expression for SP:
\[ \text{Loss} = CP - \left(\frac{19}{29} \times CP\right) \]
\[ \text{Loss} = CP \left(1 - \frac{19}{29}\right) \]
\[ \text{Loss} = CP \left(\frac{29 - 19}{29}\right) \]
\[ \text{Loss} = CP \left(\frac{10}{29}\right) \]

### Step 4: Calculate the loss percentage
The loss percentage can be calculated using the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{CP}\right) \times 100 \]

Substituting the value of Loss:
\[ \text{Loss Percentage} = \left(\frac{CP \left(\frac{10}{29}\right)}{CP}\right) \times 100 \]
\[ \text{Loss Percentage} = \left(\frac{10}{29}\right) \times 100 \]

### Step 5: Perform the calculation
Calculating the loss percentage:
\[ \text{Loss Percentage} = \frac{10 \times 100}{29} \]
\[ \text{Loss Percentage} \approx 34.48\% \]

### Final Answer
The loss percentage is approximately **34.48%**.

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