Calculation of Cost of Living Index (C.L.I)

To calculate the Cost of Living Index (C.L.I), we need to use the formula:

C.L.I = (Expenditure in the given year / Expenditure in the base year) * 100

Given that the base year is 1960 and the C.L.I in 1972 is 250, we can calculate the expenditure in 1972 using the formula:

250 = (Expenditure in 1972 / Expenditure in 1960) * 100

Solving for the expenditure in 1972, we get:

Expenditure in 1972 = (250 * Expenditure in 1960) / 100

Calculation of Extra Allowances

To maintain the standard of living in 1960, x needs to receive extra allowances in 1972. We can calculate the extra allowances by subtracting the salary in 1960 from the salary required in 1972 to maintain the standard of living in 1960.

Extra allowances = Salary required in 1972 - Salary in 1960

Given that x's salary in 1960 is 500 and in 1972 is 750, we can calculate the extra allowances as follows:

Extra allowances = 750 - 500 = 250

Therefore, x needs to receive extra allowances of 250 to maintain his standard of living in 1960 in 1972.

Explanation

The Cost of Living Index (C.L.I) is a measure of the change in prices of goods and services over time. It compares the cost of a fixed basket of goods and services in a given year to the cost of the same basket in a base year.

In this case, the base year is 1960, and the C.L.I in 1972 is 250. This means that the cost of the fixed basket of goods and services in 1972 is 250% of the cost in 1960.

To maintain the standard of living in 1960, x needs to receive extra allowances in 1972. This is because the cost of living has increased from 1960 to 1972, as indicated by the C.L.I of 250.

To calculate the extra allowances, we compare x's salary in 1960 to the salary required in 1972 to maintain the standard of living in 1960. The difference between these two salaries represents the extra allowances x needs to receive in 1972.

In this case, x's salary in 1960 is 500 and the salary required in 1972 is 750. Therefore, x needs to receive extra allowances of 250 to maintain his standard of living in 1960 in 1972.