1. Find index number using Weighted average of price relatives 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:
Weighted average of price relatives method :

Item	Weight `W`	Price `p_0`	Price `p_1`	Price relatives `I=p_1/p_0 xx 100`	`IW`
A	35	16	18	`18/16 xx 100=112.5`	3937.5
B	25	40	45	`45/40 xx 100=112.5`	2812.5
C	20	60	120	`120/60 xx 100=200`	4000
D	10	80	90	`90/80 xx 100=112.5`	1125
E	20	30	45	`45/30 xx 100=150`	3000
F	15	28	35	`35/28 xx 100=125`	1875
---	---	---	---	---	---
Total	`sum W=125`				`sum IW=16750`

Index number by weighted average of price relatives method

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

`=(16750)/(125)`

`=134`

Thus, there is a rise of `(134-100)=34%` in prices

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2. Find index number using Weighted average of price relatives 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:
Weighted average of price relatives method :

Item	Weight `W`	Price `p_0`	Price `p_1`	Price relatives `I=p_1/p_0 xx 100`	`IW`
A	40	160	200	`200/160 xx 100=125`	5000
B	25	400	600	`600/400 xx 100=150`	3750
C	5	50	70	`70/50 xx 100=140`	700
D	20	10	18	`18/10 xx 100=180`	3600
E	10	2	3	`3/2 xx 100=150`	1500
---	---	---	---	---	---
Total	`sum W=100`				`sum IW=14550`

Index number by weighted average of price relatives method

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

`=(14550)/(100)`

`=145.5`

Thus, there is a rise of `(145.5-100)=45.5%` in prices

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3. Find index number using Weighted average of price relatives method

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

Solution:
Weighted average of price relatives method :

Item	Weight `W`	Price `p_0`	Price `p_1`	Price relatives `I=p_1/p_0 xx 100`	`IW`
A	40	2	2.5	`2.5/2 xx 100=125`	5000
B	20	3	3.25	`3.25/3 xx 100=108.3333`	2166.6667
C	10	1.5	1.75	`1.75/1.5 xx 100=116.6667`	1166.6667
---	---	---	---	---	---
Total	`sum W=70`				`sum IW=8333.3333`

Index number by weighted average of price relatives method

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

`=(8333.3333)/(70)`

`=119.05`

Thus, there is a rise of `(119.05-100)=19.05%` in prices

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