Using 2105 as base year, the index number for the price of a commodity in 2016 is 118.Then the index number for 2015 taking 2016 as base year is :

Options

A. (a)`84 . 74`
B. (b)`87 . 45`
C. (c)` 8 . 475`
D. (d)`847 . 5 `

Answer

To find the index number for the year 2015, taking 2016 as the base year, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the given information**:
- The index number for the price of a commodity in 2016 (P1) is given as 118.
- The base year (P0) is 2015, which is represented by an index number of 100.

2. **Set up the formula for index numbers**:
- The formula for calculating the index number is:
\[ \text{Index Number} = \left( \frac{P1}{P0} \right) \times 100 \]
- Here, we need to find the index number for 2015 using 2016 as the base year.

3. **Rearranging the formula**:
- To find the index number for 2015 (let's call it Index_2015), we can rearrange the formula:
\[ \text{Index}_\text{2015} = \left( \frac{P0}{P1} \right) \times 100 \]

4. **Substituting the values**:
- We know that P0 (index for 2015) is 100 and P1 (index for 2016) is 118. Substitute these values into the formula:
\[ \text{Index}_\text{2015} = \left( \frac{100}{118} \right) \times 100 \]

5. **Calculating the index number**:
- Perform the calculation:
\[ \text{Index}_\text{2015} = \left( \frac{100}{118} \right) \times 100 \approx 84.745 \]

6. **Final result**:
- Therefore, the index number for 2015, taking 2016 as the base year, is approximately **84.75**.