Index number for the total cost of raw materials used for the manufacturing of te commodity in 2015, using 2001 as the base year calculated as `179.94` . If the commodity was sold for Rs `1055.75 ` in 2010 , calculate the selling price in 2015 on assumption that selling prices are directly proportional to the cost or raw materials .

Answer

To solve the problem, we need to calculate the selling price of the commodity in 2015 based on the given index number and the selling price in 2010. Here's a step-by-step solution:

### Step 1: Understand the given values
- Selling price in 2010 (P0) = Rs 1055.75
- Index number for the total cost of raw materials in 2015 (using 2010 as the base year) = 179.94

### Step 2: Use the formula for index numbers
The formula for calculating the index number is given by:
\[ \text{Index Number} = \frac{P1}{P0} \times 100 \]
Where:
- \( P1 \) = Selling price in 2015
- \( P0 \) = Selling price in 2010

### Step 3: Rearranging the formula to find P1
From the index number formula, we can rearrange it to find \( P1 \):
\[ P1 = \left(\frac{\text{Index Number}}{100}\right) \times P0 \]

### Step 4: Substitute the known values into the equation
Substituting the values we have:
\[ P1 = \left(\frac{179.94}{100}\right) \times 1055.75 \]

### Step 5: Calculate P1
Now, calculate \( P1 \):
\[ P1 = 1.7994 \times 1055.75 \]
\[ P1 = 1899.71 \]

### Conclusion
Thus, the selling price of the commodity in 2015 is Rs 1899.71.

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