Calculate the price index number for the following data using weighted aggregative method:
|
Commodity |
Unit |
Weight |
Price |
|
|
Base year |
Current year |
|||
|
P |
Quintal |
14 |
90 |
120 |
|
Q |
Kg |
20 |
10 |
17 |
|
R |
Dozen |
35 |
40 |
60 |
|
S |
Litre |
15 |
50 |
93 |
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 152.77
The Weighted Aggregative Price Index ($P_{01}$) is given by:
$P_{01} = \frac{\sum p_1 W}{\sum p_0 W} \times 100$
Calculation Table:
|
Commodity |
Weight (W) |
$p_0$ (Base) |
$p_1$ (Current) |
$p_1W$ |
$p_0W$ |
|
P |
14 |
90 |
120 |
$120 \times 14 = 1680$ |
$90 \times 14 = 1260$ |
|
Q |
20 |
10 |
17 |
$17 \times 20 = 340$ |
$10 \times 20 = 200$ |
|
R |
35 |
40 |
60 |
$60 \times 35 = 2100$ |
$40 \times 35 = 1400$ |
|
S |
15 |
50 |
93 |
$93 \times 15 = 1395$ |
$50 \times 15 = 750$ |
|
Total |
|
|
|
$\sum p_1 W = 5515$ |
$\sum p_0 W = 3610$ |
Apply the formula:
$P_{01} = \frac{5515}{3610} \times 100$
$P_{01} \approx 1.5277 \times 100$
$P_{01} = 152.77$