Taking 2015 as base year with index no. 100, the price index no. on 2022 using weighted average price relative is 182 for the following data. The sum of weights is 100, then value of x is :
| Commodity | A | B | C | D |
| Price/ unit 2015 | 20 | 10 | 5 | 40 |
| Price/unit 2022 | 24 | 20 | 30 | 40 |
| Weight | 40 | x | 10 | y |
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 24
Price Relative = $\frac{Price\,in\,2022}{Price\,in\,2015}×100$
Price Relative A = $\frac{24}{20}×100=120$
Price Relative B = $\frac{20}{10}×100=200$
Price Relative C = $\frac{30}{5}×100=600$
Price Relative D = $\frac{40}{40}×100=100$
Weighted Average Price Relative = $\frac{∑(Weight\,i×Price\,Relative\,i)}{∑\,Weights}$
$⇒182=\frac{40×120+x×200+10×600+y×100}{40+x+10+y}$
$⇒-1700=18x-82y$ ....(1)
and,
$40+x+10+y=100$
$x+y=50$ ....(2)
from (1) and (2)
$18x-82(50-x)=-1700$
$100x=2400$
$x=24$