Question

Base year weights (W) and current year price relatives (I) are given in Problem. Calculate the cost of living index in:

Find y if the cost of living index is 200.

Group	Food	Clothing	Fuel & Lighting	House Rent	Miscellaneous
I	180	120	160	300	200
W	4	5	3	y	2

Answer 1

Group	I	W	IW
Food	180	4	720
Clothing	120	5	600
Fuel & Lighting	160	33	480
House Rent	300	y	300y
Miscellaneous	200	2	400
Total	–	y + 14	300y + 2200

From the table,
`sum"W" = y + 14, sum"IW" = 300y + 2200`
Now, by Family Budget Method,

CLI = `(sum"IW")/(sum"W")`

∴ 200 = `(300y + 2200)/(y + 14)`      ...[∵ CLI = 150]

∴ 200y + 2800 = 300 +2200
∴ 300y – 200y = 2800  – 2200
∴ 100y = 600
∴ y = `(600)/(100)`
∴ y = 6.