Question

The following commodities have the given price indices relative to a base of $100$. The weights are also given:

Commodity	Relative Index	Weight
Butter	181	4
Bread	116	12
Tea	110	3
Bacon	152	7

Calculate the new index for this set of commodities

• A. $132$
• B. $133$
• C. $134$
• D. $135$

Answer 1

The correct option is D $135$

New index $=\frac{{\sum }_{i=1}^4{\left(\text{Relative index}\right)}_i\times {\left(\text{Index no. Weight}\right)}_i}{{\sum }_{i=1}^4{\left(\text{weight}\right)}_i}$
$=\frac{181\times 4+116\times 12+110\times 3+152\times 7}{4+12+3+7}$
$=\frac{724+1392+330+1064}{26}$
$=\frac{3510}{26}=\frac{1755}{13}$
$=135$