1. Find Cost of living Index number by the Family budget method

Item	Quantity	Price0	Price1
A	35	16	18
B	25	40	45
C	20	60	120
D	10	80	90
E	20	30	45
F	15	28	35

Solution:
Family budget method :

Item	Quantity `q_0`	Price `p_0`	Price `p_1`	Price relatives `I=p_1/p_0 xx 100`	`W=p_0q_0`	`IW`
A	35	16	18	112.5	560	63000
B	25	40	45	112.5	1000	112500
C	20	60	120	200	1200	240000
D	10	80	90	112.5	800	90000
E	20	30	45	150	600	90000
F	15	28	35	125	420	52500
---	---	---	---	---	---	---
Total					`sum W=4580`	`sum IW=648000`

Consumer price index number by family budget method

`I=(sum IW)/(sum W)`

`=(648000)/(4580)`

`=141.48`

Thus, there is a rise of `(141.48-100)=41.48%` in family budget

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2. Find Cost of living Index number by the Family budget method

Item	Quantity	Price0	Price1
A	40	160	200
B	25	400	600
C	5	50	70
D	20	10	18
E	10	2	3

Solution:
Family budget method :

Item	Quantity `q_0`	Price `p_0`	Price `p_1`	Price relatives `I=p_1/p_0 xx 100`	`W=p_0q_0`	`IW`
A	40	160	200	125	6400	800000
B	25	400	600	150	10000	1500000
C	5	50	70	140	250	35000
D	20	10	18	180	200	36000
E	10	2	3	150	20	3000
---	---	---	---	---	---	---
Total					`sum W=16870`	`sum IW=2374000`

Consumer price index number by family budget method

`I=(sum IW)/(sum W)`

`=(2374000)/(16870)`

`=140.72`

Thus, there is a rise of `(140.72-100)=40.72%` in family budget

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3. Find Cost of living Index number by the Family budget method

Item	Quantity	Price0	Price1
A	40	2	2.50
B	20	3	3.25
C	10	1.5	1.75

Solution:
Family budget method :

Item	Quantity `q_0`	Price `p_0`	Price `p_1`	Price relatives `I=p_1/p_0 xx 100`	`W=p_0q_0`	`IW`
A	40	2	2.5	125	80	10000
B	20	3	3.25	108.3333	60	6500
C	10	1.5	1.75	116.6667	15	1750
---	---	---	---	---	---	---
Total					`sum W=155`	`sum IW=18250`

Consumer price index number by family budget method

`I=(sum IW)/(sum W)`

`=(18250)/(155)`

`=117.74`

Thus, there is a rise of `(117.74-100)=17.74%` in family budget

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