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

Options

A. 0
B. 0.25
C. 0.2
D. `25/4` %

Answer

To solve the problem, we need to analyze the changes in the number of employees and the wages per head, and then calculate the overall effect on total wages.

### Step-by-Step Solution:

1. **Understand the Initial Conditions**:
- Let the initial number of employees be \( E \).
- Let the initial wage per employee be \( W \).
- Therefore, the initial total wages \( T \) can be calculated as:
\[ T = E \times W \]

2. **Calculate the New Number of Employees**:
- The number of employees increases by 25%. Thus, the new number of employees \( E' \) is:
\[ E' = E + 0.25E = 1.25E \]

3. **Calculate the New Wage per Employee**:
- The wage per employee decreases by 25%. Thus, the new wage per employee \( W' \) is:
\[ W' = W - 0.25W = 0.75W \]

4. **Calculate the New Total Wages**:
- The new total wages \( T' \) can be calculated as:
\[ T' = E' \times W' = (1.25E) \times (0.75W) = 0.9375E \times W \]

5. **Calculate the Percentage Decrease in Total Wages**:
- The initial total wages \( T \) is \( E \times W \).
- The new total wages \( T' \) is \( 0.9375E \times W \).
- The decrease in total wages is:
\[ \text{Decrease} = T - T' = (E \times W) - (0.9375E \times W) = 0.0625E \times W \]
- The percentage decrease \( x \) can be calculated using the formula:
\[ x = \left( \frac{\text{Decrease}}{T} \right) \times 100 = \left( \frac{0.0625E \times W}{E \times W} \right) \times 100 \]
- Simplifying this gives:
\[ x = 0.0625 \times 100 = 6.25\% \]

### Final Answer:
The value of \( x \) is \( 6.25\% \).

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