1. Find Kelly'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`	`q_k=(q_0+q_1)/2`	`p_0q_k`	`p_1q_k`
Rice	39	1	40	1.5	1.25	48.75	50
Milk	40	12	44	10	11	440	484
Bread	45	2	50	1.5	1.75	78.75	87.5
Banana	30	2	36	1.5	1.75	52.5	63
---	---	---	---	---	---	---	---
Total						`620`	`684.5`

1. By Kelly's Method, price index number

`I_K=(sum p_1q_k)/(sum p_0q_k) xx 100`

`=(684.5)/(620) xx 100`

`=110.4`

Thus, there is a rise of `(110.4-100)=10.4%` in prices

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2. Find Kelly'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`	`q_k=(q_0+q_1)/2`	`p_0q_k`	`p_1q_k`
A	10	20	12	22	21	210	252
B	8	16	8	18	17	136	136
C	5	10	6	11	10.5	52.5	63
D	4	7	4	8	7.5	30	30
---	---	---	---	---	---	---	---
Total						`428.5`	`481`

1. By Kelly's Method, price index number

`I_K=(sum p_1q_k)/(sum p_0q_k) xx 100`

`=(481)/(428.5) xx 100`

`=112.25`

Thus, there is a rise of `(112.25-100)=12.25%` in prices

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3. Find Kelly'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`	`q_k=(q_0+q_1)/2`	`p_0q_k`	`p_1q_k`
A	3	25	5	28	26.5	79.5	132.5
B	1	50	3	60	55	55	165
C	2	30	1	30	30	60	30
D	5	15	6	12	13.5	67.5	81
---	---	---	---	---	---	---	---
Total						`262`	`408.5`

1. By Kelly's Method, price index number

`I_K=(sum p_1q_k)/(sum p_0q_k) xx 100`

`=(408.5)/(262) xx 100`

`=155.92`

Thus, there is a rise of `(155.92-100)=55.92%` in prices

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