Number of employees in a factory decreases in the ratio of `8:7` and salary of employees increase in the ratio of ` 5:6`. Find whether the total salary given to the employees is increased or decreased and in what ratio ?

Options

A. `19:20`, increased
B. `20:19`, decreased
C. `19:21`, increased
D. `21:20`, decreased

Explanation

To determine whether the total salary given to the employees has increased or decreased, and in what ratio, we can follow these steps:

### Step 1: Define the initial conditions
Let the initial number of employees be represented as \( 8x \) and the initial salary per employee as \( 5y \).

### Step 2: Calculate the initial total salary
The initial total salary can be calculated as:
\[ \text{Initial Total Salary} = \text{Number of Employees} \times \text{Salary per Employee} = 8x \times 5y = 40xy \]

### Step 3: Define the new conditions after changes
According to the problem, the number of employees decreases in the ratio of \( 8:7 \), so the new number of employees will be:
\[ \text{New Number of Employees} = 7x \]
The salary of employees increases in the ratio of \( 5:6 \), so the new salary per employee will be:
\[ \text{New Salary per Employee} = 6y \]

### Step 4: Calculate the new total salary
The new total salary can be calculated as:
\[ \text{New Total Salary} = \text{New Number of Employees} \times \text{New Salary per Employee} = 7x \times 6y = 42xy \]

### Step 5: Compare the initial and new total salaries
Now we can compare the initial total salary \( 40xy \) with the new total salary \( 42xy \).

### Step 6: Determine the change in total salary
To find whether the total salary has increased or decreased, we can calculate the difference:
\[ \text{Change in Total Salary} = \text{New Total Salary} - \text{Initial Total Salary} = 42xy - 40xy = 2xy \]
Since \( 2xy \) is positive, it indicates that the total salary has increased.

### Step 7: Calculate the ratio of the total salaries
To find the ratio of the new total salary to the initial total salary:
\[ \text{Ratio} = \frac{\text{New Total Salary}}{\text{Initial Total Salary}} = \frac{42xy}{40xy} = \frac{42}{40} = \frac{21}{20} \]

### Conclusion
The total salary given to the employees has increased in the ratio of \( 21:20 \).

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