A person bought some article at rate of 36 for Rs 189 and sold them at the rate of 45 for Rs 189. Find the profit or loss percent ?

Answer

To solve the problem step by step, we will calculate the cost price (CP) and selling price (SP) per article, and then determine the profit or loss percentage.

### Step 1: Calculate the Cost Price (CP) per article
The person bought 36 articles for Rs 189.

\[ \text{Cost Price (CP) of 1 article} = \frac{\text{Total Cost Price}}{\text{Number of articles}} = \frac{189}{36} \]

### Step 2: Calculate the Selling Price (SP) per article
The person sold 45 articles for Rs 189.

\[ \text{Selling Price (SP) of 1 article} = \frac{\text{Total Selling Price}}{\text{Number of articles}} = \frac{189}{45} \]

### Step 3: Simplify the Cost Price and Selling Price
Now we will simplify both CP and SP.

1. **Cost Price (CP)**:
\[ CP = \frac{189}{36} = 5.25 \text{ Rs (approximately)} \]

2. **Selling Price (SP)**:
\[ SP = \frac{189}{45} = 4.20 \text{ Rs (approximately)} \]

### Step 4: Determine Profit or Loss
Now we can determine whether there is a profit or a loss by comparing CP and SP.

- Since \( CP > SP \), there is a loss.

### Step 5: Calculate the Loss Amount
\[ \text{Loss} = CP - SP = 5.25 - 4.20 = 1.05 \text{ Rs} \]

### Step 6: Calculate the Loss Percentage
The formula for loss percentage is:

\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100 \]

Substituting the values we have:

\[ \text{Loss Percentage} = \left( \frac{1.05}{5.25} \right) \times 100 \]

Calculating this gives:

\[ \text{Loss Percentage} = 20\% \]

### Final Answer
The loss percentage is **20%**.

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