Step-by-step explanation:
Given
During the certain period the C.L.I. goes up from 110 to 200 and the Salary of a worker is also raised from 330 to 500
Cost of living in certain period = 110
Cost of living in current year = 200
Salary of worker in certain period = 330
Salary of worker in current year = 500
Real wages for a certain period
= money wages in certain period / cost of living in certain period x 100
= 330 / 110 x 100
= 3 x 100 = 300
Real wages for current year = money wages in current year/ cost of living in current year x 100
= 500 / 200 x 100
= 2.5 x 100
= 250
So we can conclude that wage of worker had increased from 330 to 500 but his real wage had dropped from Rs 300 to Rs 250. So in real terms it is a loss of Rs 50

If you are using the above method, you need to multiply your final answer by 2. For eg., In the above answer, the final answer was Rs.50. So, you need to multiply that 50 by 2. I tried this with different sums and got the correct answer by my method. You can also try my method.

Introduction
During a certain period, the cost of living index number increased from 110 to 200, and the salary of a worker also increased from 330 to 500. However, the worker did not experience a real gain in wages. We need to calculate the decrease in real wages and determine the correct option.

Understanding the Problem
To understand the problem, we need to first grasp the concept of the cost of living index number and real wages. The cost of living index number measures the relative cost of living over time, indicating how much prices have increased or decreased. Real wages, on the other hand, reflect the actual purchasing power of wages after adjusting for inflation.

Calculating the Increase in the Cost of Living Index
To calculate the increase in the cost of living index, we subtract the initial index from the final index:
Increase in Cost of Living Index = Final Index - Initial Index
Increase in Cost of Living Index = 200 - 110
Increase in Cost of Living Index = 90

Calculating the Increase in Salary
To calculate the increase in salary, we subtract the initial salary from the final salary:
Increase in Salary = Final Salary - Initial Salary
Increase in Salary = 500 - 330
Increase in Salary = 170

Calculating the Decrease in Real Wages
To calculate the decrease in real wages, we need to adjust the increase in salary based on the increase in the cost of living index. This adjustment is done by dividing the increase in salary by the increase in the cost of living index and multiplying by 100:
Decrease in Real Wages = (Increase in Salary / Increase in Cost of Living Index) * 100
Decrease in Real Wages = (170 / 90) * 100
Decrease in Real Wages = 188.88

Determining the Correct Option
Based on the calculations, we can see that the real wages decreased by approximately 188.88. None of the given options (a) 45.45, (b) 43.25, (c) 100 match the calculated value. Therefore, the correct option is (d) None of these.

Conclusion
The worker experienced a decrease in real wages due to the increase in the cost of living index. The correct option is (d) None of these, as none of the provided options match the calculated decrease in real wages.