The selling price of 15 articles is equal to the cost price of 12 articles. Find the gain or loss as percent

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Understand the relationship between selling price and cost price.
We know that the selling price (SP) of 15 articles is equal to the cost price (CP) of 12 articles.

### Step 2: Assign a value to the cost price of one article.
Let’s assume the cost price of one article is ₹1. Therefore, the cost price of 12 articles can be calculated as:
\[ \text{Cost Price of 12 articles} = 12 \times \text{Cost Price of 1 article} = 12 \times 1 = ₹12 \]

### Step 3: Determine the selling price of 15 articles.
Since the selling price of 15 articles is equal to the cost price of 12 articles, we have:
\[ \text{Selling Price of 15 articles} = ₹12 \]

### Step 4: Calculate the cost price of 15 articles.
The cost price of 15 articles can be calculated as:
\[ \text{Cost Price of 15 articles} = 15 \times \text{Cost Price of 1 article} = 15 \times 1 = ₹15 \]

### Step 5: Determine the loss incurred.
Now, we can find the loss by subtracting the selling price from the cost price:
\[ \text{Loss} = \text{Cost Price of 15 articles} - \text{Selling Price of 15 articles} = ₹15 - ₹12 = ₹3 \]

### Step 6: 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:
\[ \text{Loss Percentage} = \left(\frac{3}{15}\right) \times 100 = 20\% \]

### Final Answer:
The loss is 20%.

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