Question

The data about index numbers and weights for groups of items for the living of industrial workers in Ahmedabad city in the years 2014 and 2015 are as follows. Find the cost of living index number of industrial workers. If the wages of workers are increased by 5 % in the year 2015 then is this rise sufficient to compensate the rise in price in the year 2015 ?

Group	Food	Fuel and Electricity	Housing	Clothing	Miscellaneous expense
Weight	31	14	22	10	23
Index number of 2014	270	168	205	174	303
index number of 2015	281	178	210	177	337

Answer 1

Index number for the year 2014

=  239.41

Index number for the year 2015 

= 253.44

There is an increase of (253.44 – 239.41 =) 14.03 % in the cost of living expenditure of 2015 as compared to that of the year 2014.

The wages of workers are increased by 5% in the year 2015.
The actual percentage increase in the cost of living expenditure of workers in the year 2015 as compared to the year 2014

\(=\cfrac{ Percentage increase in cost of living expenditure in the year 2015}{ Cost of living index number for the year 2014 } × 100\)

\(=\frac{14.03}{239.41}\times 100\)

= 0.0586 × 100

= 5.86 %

But the increase in wage is 5 %.

Hence, the increase in the wages of workers in the year 2015 is not sufficient and is short by (5.86 – 5 =) 0.86 %.