If ` sum p_1 omega = 344 and sum p_2omega =408 `, then find the price index number.

Answer

To find the price index number given the values of \( \sum P_1 \omega = 344 \) and \( \sum P_2 \omega = 408 \), we will follow these steps:

### Step 1: Write down the formula for the price index number.
The formula for the price index number (PIN) is given by:

\[ \text{Price Index Number} = \frac{\sum P_2 \omega}{\sum P_1 \omega} \times 100 \]

### Step 2: Substitute the given values into the formula.
We know that:

- \( \sum P_1 \omega = 344 \)
- \( \sum P_2 \omega = 408 \)

Substituting these values into the formula gives:

\[ \text{Price Index Number} = \frac{408}{344} \times 100 \]

### Step 3: Calculate the fraction.
Now, we will calculate the fraction \( \frac{408}{344} \):

\[ \frac{408}{344} = 1.1884 \quad (\text{approximately}) \]

### Step 4: Multiply by 100.
Now, we multiply the result by 100 to find the price index number:

\[ \text{Price Index Number} = 1.1884 \times 100 = 118.84 \]

### Step 5: Round the result.
Rounding to two decimal places, we get:

\[ \text{Price Index Number} \approx 118.84 \]

### Final Answer:
Thus, the required price index number is:

\[ \text{Price Index Number} = 118.84 \]

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