The number of employees working in a farm is increased by 25% and the wages per head ar decreased by 25%. If it results in x% decrease in total wages, then the value of x is

Options

A. 0
B. 25
C. 20
D. `25/4`

Answer

To solve the problem, we need to determine the percentage decrease in total wages when the number of employees increases by 25% and the wages per head decrease by 25%.

Let's break it down step by step:

### Step 1: Define Variables
Let:
- \( x \) = original number of employees
- \( y \) = original wage per employee

### Step 2: Calculate New Number of Employees
The number of employees is increased by 25%. Therefore, the new number of employees will be:
\[ \text{New number of employees} = x + 0.25x = 1.25x \]

### Step 3: Calculate New Wage per Employee
The wage per employee is decreased by 25%. Therefore, the new wage per employee will be:
\[ \text{New wage per employee} = y - 0.25y = 0.75y \]

### Step 4: Calculate Total Wages Before and After Changes
- **Total wages before changes**:
\[ \text{Total wages (original)} = x \cdot y \]

- **Total wages after changes**:
\[ \text{Total wages (new)} = \text{New number of employees} \times \text{New wage per employee} = (1.25x) \cdot (0.75y) = 0.9375xy \]

### Step 5: Calculate the Change in Total Wages
To find the decrease in total wages, we subtract the new total wages from the original total wages:
\[ \text{Decrease in total wages} = xy - 0.9375xy = (1 - 0.9375)xy = 0.0625xy \]

### Step 6: Calculate the Percentage Decrease in Total Wages
The percentage decrease in total wages is given by:
\[ \text{Percentage decrease} = \left( \frac{\text{Decrease in total wages}}{\text{Total wages (original)}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage decrease} = \left( \frac{0.0625xy}{xy} \right) \times 100 = 0.0625 \times 100 = 6.25\% \]

### Conclusion
Thus, the value of \( x \) (the percentage decrease in total wages) is:
\[ \boxed{6.25\%} \]