Index number calculated for the year 2019 using 2015 as the base year is `114.9` .If commodity is sold for Rs `5.75` in 2015 , then the selling price in 2019 is

Options

A. Rs `7.57`
B. Rs `6.61 `
C. Rs` 6.16`
D. Rs `66.1 `

Answer

To find the selling price of the commodity in the year 2019, we can use the concept of index numbers. Here are the steps to solve the problem:

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Index number for 2019 (using 2015 as the base year) = 114.9
- Selling price in 2015 (P0) = Rs 5.75

2. **Use the Formula for Index Number:**
The formula for calculating the index number is:
\[ \text{Index Number} = \left( \frac{P1}{P0} \right) \times 100 \]
where:
- \( P1 \) = Price in the current year (2019)
- \( P0 \) = Price in the base year (2015)

3. **Substitute the Known Values into the Formula:**
We can rearrange the formula to solve for \( P1 \):
\[ 114.9 = \left( \frac{P1}{5.75} \right) \times 100 \]

4. **Isolate \( P1 \):**
To isolate \( P1 \), we first divide both sides by 100:
\[ \frac{114.9}{100} = \frac{P1}{5.75} \]
This simplifies to:
\[ 1.149 = \frac{P1}{5.75} \]

5. **Multiply Both Sides by 5.75:**
Now, multiply both sides by 5.75 to find \( P1 \):
\[ P1 = 1.149 \times 5.75 \]

6. **Calculate \( P1 \):**
Performing the multiplication:
\[ P1 = 6.60675 \]

7. **Round the Result:**
Rounding to two decimal places, we get:
\[ P1 \approx 6.61 \]

### Final Answer:
The selling price of the commodity in 2019 is approximately Rs 6.61.

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