If the cost price of 12 articles be equal to the selling price of 20 articles, then find the loss percent in the transaction.

Options

A. 16
B. 20
C. 25
D. 26

Answer

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

### Step 1: Define Variables
Let the cost price (CP) of one article be \( C \) and the selling price (SP) of one article be \( S \).

### Step 2: Set Up the Equation
According to the problem, the cost price of 12 articles is equal to the selling price of 20 articles. We can express this as:
\[ 12C = 20S \]

### Step 3: Simplify the Equation
To simplify the equation, we can divide both sides by 4:
\[ 3C = 5S \]

### Step 4: Find the Ratio of Selling Price to Cost Price
From the equation \( 3C = 5S \), we can rearrange it to find the ratio of \( S \) to \( C \):
\[ \frac{S}{C} = \frac{3}{5} \]

### Step 5: Assign Values to CP and SP
To make calculations easier, let's assume the cost price of one article \( C \) is Rs. 5. Then, we can find the selling price \( S \):
\[ S = \frac{3}{5} \times C = \frac{3}{5} \times 5 = 3 \]
So, the selling price of one article is Rs. 3.

### Step 6: Calculate the Loss
Now we can calculate the loss incurred in the transaction:
\[ \text{Loss} = \text{Cost Price} - \text{Selling Price} = C - S = 5 - 3 = 2 \]

### Step 7: Calculate the Loss Percentage
To find the loss percentage, we use the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Loss Percentage} = \left( \frac{2}{5} \right) \times 100 = 40\% \]

### Final Answer
The loss percent in the transaction is **40%**.

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