Number of employees in a factory decreases in the ratio of 8 : 7 and salary of employees increases in the ratio of 5:6. Find wheather the total salary given to the empolyees 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

Answer

To solve the problem, we need to analyze the changes in the number of employees and their salaries, and then calculate the total salary before and after these changes.

### Step-by-Step Solution:

1. **Define Variables for Employees and Salaries:**
- Let the initial number of employees be represented as \(8K\) (where \(K\) is a common multiplier).
- Let the initial salary per employee be represented as \(5L\) (where \(L\) is another common multiplier).

2. **Calculate Initial Total Salary:**
- The total initial salary can be calculated as:
\[ \text{Initial Total Salary} = \text{Number of Employees} \times \text{Salary per Employee} = 8K \times 5L = 40KL \]

3. **Determine the Present Number of Employees:**
- The number of employees decreases in the ratio of \(8:7\), so the present number of employees is:
\[ \text{Present Number of Employees} = 7K \]

4. **Determine the Present Salary per Employee:**
- The salary increases in the ratio of \(5:6\), so the present salary per employee is:
\[ \text{Present Salary per Employee} = 6L \]

5. **Calculate Present Total Salary:**
- The total present salary can be calculated as:
\[ \text{Present Total Salary} = \text{Present Number of Employees} \times \text{Present Salary per Employee} = 7K \times 6L = 42KL \]

6. **Compare Initial and Present Total Salaries:**
- We now have:
- Initial Total Salary = \(40KL\)
- Present Total Salary = \(42KL\)

7. **Determine the Change in Total Salary:**
- To find out whether the total salary has increased or decreased, we compare the two:
\[ \text{Change in Salary} = \text{Present Total Salary} - \text{Initial Total Salary} = 42KL - 40KL = 2KL \]
- Since \(2KL\) is positive, the total salary has increased.

8. **Calculate the Ratio of Increase:**
- The ratio of the initial total salary to the present total salary is:
\[ \text{Ratio} = \frac{\text{Initial Total Salary}}{\text{Present Total Salary}} = \frac{40KL}{42KL} = \frac{40}{42} = \frac{20}{21} \]

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

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