Selling price of 33 articles is equal to cost price of 44 articles. Find profit/loss percent?

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the relationship between Selling Price (SP) and Cost Price (CP)
We know from the problem that the Selling Price of 33 articles is equal to the Cost Price of 44 articles.

### Step 2: Set up the equation
Let the Cost Price of one article be \( CP = K \). Therefore, the Cost Price of 44 articles will be:
\[ CP_{44} = 44K \]

Let the Selling Price of one article be \( SP = S \). Therefore, the Selling Price of 33 articles will be:
\[ SP_{33} = 33S \]

According to the problem:
\[ SP_{33} = CP_{44} \]
So we have:
\[ 33S = 44K \]

### Step 3: Find the ratio of Selling Price to Cost Price
To find the ratio of Selling Price to Cost Price, we can rearrange the equation:
\[ \frac{S}{K} = \frac{44}{33} \]

### Step 4: Simplify the ratio
Now, simplify \( \frac{44}{33} \):
\[ \frac{44}{33} = \frac{4}{3} \]

This means:
\[ \frac{S}{K} = \frac{4}{3} \]

### Step 5: Express Selling Price and Cost Price in terms of a common factor
Let’s denote the common factor as \( K \):
- Selling Price (SP) = \( 4K \)
- Cost Price (CP) = \( 3K \)

### Step 6: Calculate Profit
Profit is calculated as:
\[ \text{Profit} = SP - CP \]
Substituting the values:
\[ \text{Profit} = 4K - 3K = K \]

### Step 7: Calculate Profit Percentage
Profit Percentage is given by the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{K}{3K} \right) \times 100 \]

### Step 8: Simplify the Profit Percentage
This simplifies to:
\[ \text{Profit Percentage} = \frac{1}{3} \times 100 = 33.33\% \]

### Final Answer
Thus, the profit percentage is:
\[ \text{Profit Percentage} = 33 \frac{1}{3} \% \]

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