The price relatives and weights of a set of commodities are given as:
| Commodity | P | Q | R |
| Price Relative | 100 | 130 | 180 |
| Weight | x | 2x | y |
If the sum of weights is 54 and index for the set is 130, then the values of x and y are
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → x = 15, y = 9
The index for the set is the weighted average of the price relatives:
\( \displaystyle \text{Index} = \frac{\Sigma (\text{price relative} \times \text{weight})}{\Sigma \text{weight}} \)
The sum of weights is 54:
\(x + 2x + y = 54\)
\(3x + y = 54\)
The index is 130:
\( \displaystyle \frac{100x + 130(2x) + 180y}{54} = 130 \)
\(360x + 180y = 7020\)
\(2x + y = 39\)
Subtracting this from 3x + y = 54:
\(x = 15\)
\(y = 54 - 45 = 9\)
Note: This topic was not in the CUET 2026 syllabus.