There are 30 workers in a factory. If the number of workers increases by 10, then the total wages increased by Rs. 9000 per day while the average wages per worker decreases by Rs. 75. Find the original total wages of factory.

Answer

To solve the problem, we need to find the original total wages of the factory. Let's break it down step by step.

### Step 1: Define Variables
Let:
- \( W \) = original total wages of the factory
- \( A \) = original average wage per worker

Since there are 30 workers, we can express the total wages as:
\[ W = 30A \]

### Step 2: Analyze the Change in Workers and Wages
When the number of workers increases by 10, the total number of workers becomes:
\[ 30 + 10 = 40 \]

The total wages increase by Rs. 9000, so the new total wages become:
\[ W + 9000 \]

### Step 3: Calculate the New Average Wage
The new average wage per worker after the increase in workers is:
\[ \text{New Average Wage} = \frac{W + 9000}{40} \]

### Step 4: Set Up the Equation for Average Wage Decrease
According to the problem, the average wage per worker decreases by Rs. 75. Therefore, we can write:
\[ \text{New Average Wage} = A - 75 \]

### Step 5: Equate the Two Expressions for New Average Wage
Now we have two expressions for the new average wage:
1. \( \frac{W + 9000}{40} \)
2. \( A - 75 \)

Setting them equal gives us:
\[ \frac{W + 9000}{40} = A - 75 \]

### Step 6: Substitute \( W \) in Terms of \( A \)
We know \( W = 30A \), so we substitute this into the equation:
\[ \frac{30A + 9000}{40} = A - 75 \]

### Step 7: Clear the Fraction
Multiply both sides by 40 to eliminate the fraction:
\[ 30A + 9000 = 40(A - 75) \]

### Step 8: Expand and Simplify
Expanding the right side:
\[ 30A + 9000 = 40A - 3000 \]

### Step 9: Rearrange the Equation
Rearranging gives:
\[ 9000 + 3000 = 40A - 30A \]
\[ 12000 = 10A \]

### Step 10: Solve for \( A \)
Dividing both sides by 10:
\[ A = 1200 \]

### Step 11: Find the Original Total Wages
Now that we have the average wage, we can find the original total wages:
\[ W = 30A = 30 \times 1200 = 36000 \]

### Final Answer
The original total wages of the factory is Rs. 36,000.

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