Using simple average of price relatives method, the price index for 2010, taking 2001 as base year was found to be 127. If `SigmaI=612+(50x)/(9)` and number of commondities = 6 then find the value of x .

Options

A. 20
B. 27
C. 25
D. 29

Answer

To find the value of \( x \) using the given information, we can follow these steps:

### Step 1: Write down the known values
We know:
- Price index \( P = 127 \)
- \( \Sigma I = 612 + \frac{50x}{9} \)
- Number of commodities \( n = 6 \)

### Step 2: Use the formula for the price index
The formula for the price index using the simple average of price relatives method is given by:

\[ P = \frac{1}{n} \Sigma I \]

Substituting the known values into the formula:

\[ 127 = \frac{1}{6} \left( 612 + \frac{50x}{9} \right) \]

### Step 3: Multiply both sides by 6
To eliminate the fraction, multiply both sides by 6:

\[ 127 \times 6 = 612 + \frac{50x}{9} \]

Calculating \( 127 \times 6 \):

\[ 762 = 612 + \frac{50x}{9} \]

### Step 4: Isolate \( \frac{50x}{9} \)
Now, subtract 612 from both sides:

\[ 762 - 612 = \frac{50x}{9} \]

Calculating \( 762 - 612 \):

\[ 150 = \frac{50x}{9} \]

### Step 5: Solve for \( x \)
To solve for \( x \), multiply both sides by 9:

\[ 150 \times 9 = 50x \]

Calculating \( 150 \times 9 \):

\[ 1350 = 50x \]

Now, divide both sides by 50:

\[ x = \frac{1350}{50} \]

Calculating \( \frac{1350}{50} \):

\[ x = 27 \]

### Final Answer
Thus, the value of \( x \) is:

\[ \boxed{27} \]