1. Find Laspeyre's index number, Paasche's index number, Dorbish-Bowley's index number

Item	Price0	Quantity0	Price1	Quantity1
Rice	39	1	40	1.5
Milk	40	12	44	10
Bread	45	2	50	1.5
Banana	30	2	36	1.5

Solution:

Item	`p_0`	`q_0`	`p_1`	`q_1`	`p_1q_0`	`p_0q_0`	`p_1q_1`	`p_0q_1`
Rice	39	1	40	1.5	40	39	60	58.5
Milk	40	12	44	10	528	480	440	400
Bread	45	2	50	1.5	100	90	75	67.5
Banana	30	2	36	1.5	72	60	54	45
---	---	---	---	---	---	---	---	---
Total					`740`	`669`	`629`	`571`

1. Laspeyre's index number

`I_L=(sum p_1q_0)/(sum p_0q_0) xx 100`

`=(740)/(669) xx 100`

`=110.61`

Thus, there is a rise of `(110.61-100)=10.61%` in prices

---

2. Paasche's index number

`I_P=(sum p_1q_1)/(sum p_0q_1) xx 100`

`=(629)/(571) xx 100`

`=110.16`

Thus, there is a rise of `(110.16-100)=10.16%` in prices

---

3. Dorbish and Bowley's price index

`I_D=(I_L + I_P)/2`

`=(110.6129+110.1576)/2`

`=(220.7705)/2`

`=110.39`

Thus, there is a rise of `(110.39-100)=10.39%` in prices

---

2. Find Dorbish-Bowley's index number

Item	Price0	Quantity0	Price1	Quantity1
A	10	20	12	22
B	8	16	8	18
C	5	10	6	11
D	4	7	4	8

Solution:

Item	`p_0`	`q_0`	`p_1`	`q_1`	`p_1q_0`	`p_0q_0`	`p_1q_1`	`p_0q_1`
A	10	20	12	22	240	200	264	220
B	8	16	8	18	128	128	144	144
C	5	10	6	11	60	50	66	55
D	4	7	4	8	28	28	32	32
---	---	---	---	---	---	---	---	---
Total					`456`	`406`	`506`	`451`

1. Dorbish and Bowley's price index

`I_D=((sum p_1q_0)/(sum p_0q_0) + (sum p_1q_1)/(sum p_0q_1))/2 xx 100`

`=((456)/(406) + (506)/(451))/2 xx 100`

`=(2.2451)/2 xx 100`

`=1.1226 xx 100`

`=112.26`

Thus, there is a rise of `(112.26-100)=12.26%` in prices

---

3. Find Dorbish-Bowley's index number

Item	Price0	Quantity0	Price1	Quantity1
A	3	25	5	28
B	1	50	3	60
C	2	30	1	30
D	5	15	6	12

Solution:

Item	`p_0`	`q_0`	`p_1`	`q_1`	`p_1q_0`	`p_0q_0`	`p_1q_1`	`p_0q_1`
A	3	25	5	28	125	75	140	84
B	1	50	3	60	150	50	180	60
C	2	30	1	30	30	60	30	60
D	5	15	6	12	90	75	72	60
---	---	---	---	---	---	---	---	---
Total					`395`	`260`	`422`	`264`

1. Dorbish and Bowley's price index

`I_D=((sum p_1q_0)/(sum p_0q_0) + (sum p_1q_1)/(sum p_0q_1))/2 xx 100`

`=((395)/(260) + (422)/(264))/2 xx 100`

`=(3.1177)/2 xx 100`

`=1.5589 xx 100`

`=155.89`

Thus, there is a rise of `(155.89-100)=55.89%` in prices

---

---