A person bought some article at rate of 5 for Rs 1 and bought same number of articles at the rate of 4 for Rs 1. And sold all the stock at the rate of 9 for Rs 2.Total loss is 3 rupees.Find the number of articles he bought?

Answer

To solve the problem, we will break it down step by step.

### Step 1: Define Variables
Let the number of articles bought in each case be \( x \).

### Step 2: Calculate the Cost of Articles
1. **First Purchase**: The person bought \( x \) articles at the rate of 5 for Rs 1.
- Cost of \( x \) articles = \( \frac{x}{5} \) rupees.

2. **Second Purchase**: The person bought the same number \( x \) articles at the rate of 4 for Rs 1.
- Cost of \( x \) articles = \( \frac{x}{4} \) rupees.

### Step 3: Total Cost Calculation
- Total cost for both purchases:
\[ \text{Total Cost} = \frac{x}{5} + \frac{x}{4} \]
- To add these fractions, find a common denominator (which is 20):
\[ \text{Total Cost} = \frac{4x}{20} + \frac{5x}{20} = \frac{9x}{20} \text{ rupees} \]

### Step 4: Calculate Selling Price
- The person sold all \( 2x \) articles (since he bought \( x \) articles twice) at the rate of 9 for Rs 2.
- Selling price for \( 2x \) articles:
\[ \text{Selling Price} = \frac{2x}{9} \times 2 = \frac{4x}{9} \text{ rupees} \]

### Step 5: Calculate Loss
- According to the problem, the total loss is Rs 3.
- Loss can be calculated as:
\[ \text{Loss} = \text{Total Cost} - \text{Selling Price} \]
- Therefore:
\[ \frac{9x}{20} - \frac{4x}{9} = 3 \]

### Step 6: Solve the Equation
1. Find a common denominator for the left side (which is 180):
\[ \frac{9x \times 9}{180} - \frac{4x \times 20}{180} = 3 \]
\[ \frac{81x - 80x}{180} = 3 \]
\[ \frac{x}{180} = 3 \]
\[ x = 3 \times 180 = 540 \]

### Step 7: Conclusion
The total number of articles he bought is \( 540 \).