The wages of labourers in a factory increased in the ratio 22 : 25 and there was a reduction in their number in the ratio 15 : 11. Find the original wages bill if the present wages is Rs 5000

Options

A. `Rs2500`
B. `Rs3000`
C. `Rs5000`
D. `Rs6000`

Answer

To solve the problem step by step, we will follow the ratios given and calculate the original wages bill based on the present wages.

### Step 1: Understand the Ratios
The wages of laborers increased in the ratio of 22:25, and the number of laborers decreased in the ratio of 15:11.

### Step 2: Set Up the Ratios
Let:
- Original wages per laborer = 22x
- Present wages per laborer = 25x
- Original number of laborers = 15y
- Present number of laborers = 11y

### Step 3: Calculate the Total Wages
The total wages bill can be calculated using the formula:
\[ \text{Total Wages Bill} = \text{Wages per laborer} \times \text{Number of laborers} \]

- Original wages bill = (Original wages per laborer) × (Original number of laborers)
- Present wages bill = (Present wages per laborer) × (Present number of laborers)

### Step 4: Set Up the Equation
From the problem, we know that the present wages bill is Rs 5000. Therefore, we can set up the equation:
\[ 25x \times 11y = 5000 \]

### Step 5: Simplify the Equation
Now, simplify the equation:
\[ 275xy = 5000 \]
\[ xy = \frac{5000}{275} \]
\[ xy = 18.18 \] (approximately)

### Step 6: Find the Original Wages Bill
Now, we need to find the original wages bill:
\[ \text{Original Wages Bill} = 22x \times 15y \]
\[ = 330xy \]

### Step 7: Substitute the Value of xy
Now substitute the value of \( xy \):
\[ = 330 \times 18.18 \]
\[ = 6000 \]

### Conclusion
The original wages bill is Rs 6000.