In an office the number of employees reduces in the ratio of 3: 2and the wages increases in the ratio of 20: 27 What is the profit percentage of employees over the previous wages?

Options

A. `10%`
B. `9.09%`
C. `11.11%`
D. none of these

Answer

To solve the problem step by step, we need to analyze the changes in the number of employees and their wages.

### Step 1: Understand the Ratios
The number of employees reduces in the ratio of 3:2. This means for every 3 employees previously, there are now 2 employees.

### Step 2: Assign Values to Employees
Let's assume the initial number of employees is 3x (where x is a common multiplier). After the reduction, the number of employees becomes 2x.

### Step 3: Understand Wage Ratios
The wages increase in the ratio of 20:27. This means for every 20 units of wages previously, the new wages are 27 units.

### Step 4: Assign Values to Wages
Let's assume the initial total wages paid to employees is 20y (where y is a common multiplier). After the increase, the total wages become 27y.

### Step 5: Calculate Initial and New Total Wages
- Initial total wages = 20y
- New total wages = 27y

### Step 6: Calculate the Change in Wages
The change in wages is:
\[ \text{Change in wages} = \text{New wages} - \text{Initial wages} = 27y - 20y = 7y \]

### Step 7: Calculate the Profit Percentage
The profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Change in wages}}{\text{Initial wages}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{7y}{20y} \right) \times 100 = \left( \frac{7}{20} \right) \times 100 = 35\% \]

### Final Answer
The profit percentage of employees over the previous wages is **35%**.