The cost of living index in the year 2006, taking 2004 as the base year, on certain commodities is 162.75. If the total expenditure in 2004 was Rs. 12,500, then find the total cost for the same commodities in the year 2006.

Answer

To find the total cost for the same commodities in the year 2006, we can use the formula for the cost of living index. The formula is:

\[ \text{Cost of Living Index} = \left( \frac{\text{Total Expenditure in Current Year}}{\text{Total Expenditure in Base Year}} \right) \times 100 \]

### Step 1: Identify the Known Values
- Cost of Living Index in 2006 = 162.75
- Total Expenditure in Base Year (2004) = Rs. 12,500

### Step 2: Set Up the Equation
Using the formula for the cost of living index, we can set up the equation:

\[ 162.75 = \left( \frac{x}{12500} \right) \times 100 \]

where \( x \) is the total expenditure in the current year (2006).

### Step 3: Rearrange the Equation to Solve for \( x \)
To isolate \( x \), we first multiply both sides of the equation by 12500:

\[ 162.75 \times 12500 = x \times 100 \]

### Step 4: Calculate the Left Side
Now, calculate \( 162.75 \times 12500 \):

\[ 162.75 \times 12500 = 2034375 \]

### Step 5: Divide by 100
Now, we divide both sides by 100 to solve for \( x \):

\[ x = \frac{2034375}{100} \]

### Step 6: Calculate \( x \)
Now, calculate \( x \):

\[ x = 20343.75 \]

### Conclusion
The total cost for the same commodities in the year 2006 is Rs. 20,343.75.

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