The employer reduces the number of employees in the ratio 9: 8 and increases their wages in the ratio 14: 15. If the previous wage bill was Rs 189000, what is the amount by which the new wage bill will increase or decrease?

Options

A. Rs 21000
B. Rs 10000
C. Rs 9000
D. Rs 25000

Answer

To solve the problem, we need to analyze the changes in the number of employees and their wages, and then calculate the new wage bill.

### Step-by-Step Solution:

1. **Identify the Ratios**:
- The number of employees is reduced in the ratio of 9:8.
- The wages are increased in the ratio of 14:15.

2. **Let Initial Values**:
- Let the initial number of employees be represented as \(9x\).
- Let the initial wage of each employee be represented as \(14y\).

3. **Calculate Initial Wage Bill**:
- The initial wage bill can be calculated as:
\[ \text{Initial Wage Bill} = \text{Number of Employees} \times \text{Wage per Employee} = 9x \times 14y = 126xy \]
- We know from the problem that the initial wage bill is Rs 189,000. Therefore:
\[ 126xy = 189000 \]

4. **Solve for \(xy\)**:
- To find \(xy\), we divide both sides by 126:
\[ xy = \frac{189000}{126} = 1500 \]

5. **Calculate New Values**:
- After the changes, the number of employees becomes \(8x\) (due to the reduction).
- The new wage per employee becomes \(15y\) (due to the increase).

6. **Calculate New Wage Bill**:
- The new wage bill can be calculated as:
\[ \text{New Wage Bill} = \text{New Number of Employees} \times \text{New Wage per Employee} = 8x \times 15y = 120xy \]

7. **Substitute \(xy\) into New Wage Bill**:
- Now substitute \(xy = 1500\) into the new wage bill equation:
\[ \text{New Wage Bill} = 120 \times 1500 = 180000 \]

8. **Calculate Change in Wage Bill**:
- To find the change in the wage bill, subtract the new wage bill from the initial wage bill:
\[ \text{Change} = \text{New Wage Bill} - \text{Initial Wage Bill} = 180000 - 189000 = -9000 \]

9. **Conclusion**:
- The new wage bill has decreased by Rs 9,000.

### Final Answer:
The amount by which the new wage bill will decrease is Rs 9,000.