During a certain period , the cost of living index number goes from 110 to 200 and the salary of a worker is also raised from Rs 325 to Rs 500. Does the worker really gains or loses, and by how much amount in real terms ?

Answer

To determine whether the worker gains or loses in real terms after the salary increase, we will calculate the real wages before and after the salary change using the cost of living index numbers.

### Step-by-Step Solution:

1. **Identify the Initial and Final Values:**
- Initial cost of living index (CPI_initial) = 110
- Final cost of living index (CPI_final) = 200
- Initial salary (Salary_initial) = Rs 325
- Final salary (Salary_final) = Rs 500

2. **Calculate the Real Wage Before the Salary Increase:**
- The formula for real wage is:
\[ \text{Real Wage} = \frac{\text{Actual Wage}}{\text{Cost of Living Index}} \times 100 \]
- For the initial salary:
\[ \text{Real Wage_initial} = \frac{325}{110} \times 100 \]
- Calculating this:
\[ \text{Real Wage_initial} = \frac{32500}{110} = 295.45 \]

3. **Calculate the Real Wage After the Salary Increase:**
- For the final salary:
\[ \text{Real Wage_final} = \frac{500}{200} \times 100 \]
- Calculating this:
\[ \text{Real Wage_final} = \frac{50000}{200} = 250 \]

4. **Determine the Gain or Loss in Real Terms:**
- To find out if the worker gains or loses, subtract the real wage after the increase from the real wage before the increase:
\[ \text{Loss} = \text{Real Wage_initial} - \text{Real Wage_final} \]
- Substituting the values:
\[ \text{Loss} = 295.45 - 250 = 45.45 \]

5. **Conclusion:**
- The worker experiences a loss of Rs 45.45 in real terms.

### Final Answer:
The worker loses Rs 45.45 in real terms.