To construct the Index numbers of price, we first need to calculate the required sums from the given data. Let 1984 be the base year (denoted by subscript 0) and 1985 be the current year (denoted by s

To construct the Index numbers of price, we first need to calculate the required sums from the given data. Let 1984 be the base year (denoted by subscript 0) and 1985 be the current year (denoted by subscript 1).

The data is:

Commodities	$p_0$	$q_0$	$p_1$	$q_1$
A	4	8	8	6
B	10	10	12	5
C	8	14	10	10
D	4	19	4	13

Step 1: Calculate the necessary products and their sums.

Commodity	$p_0$	$q_0$	$p_1$	$q_1$	$p_1 q_0$	$p_0 q_0$	$p_1 q_1$	$p_0 q_1$
A	4	8	8	6	$8 \times 8 = 64$	$4 \times 8 = 32$	$8 \times 6 = 48$	$4 \times 6 = 24$
B	10	10	12	5	$12 \times 10 = 120$	$10 \times 10 = 100$	$12 \times 5 = 60$	$10 \times 5 = 50$
C	8	14	10	10	$10 \times 14 = 140$	$8 \times 14 = 112$	$10 \times 10 = 100$	$8 \times 10 = 80$
D	4	19	4	13	$4 \times 19 = 76$	$4 \times 19 = 76$	$4 \times 13 = 52$	$4 \times 13 = 52$
Sum					400	320	260	206

So, we have:
$\sum p_1 q_0 = 400$
$\sum p_0 q_0 = 320$
$\sum p_1 q_1 = 260$
$\sum p_0 q_1 = 206$

(i) Laspeyre's method
The formula for Laspeyre's Price Index ($P_L$) is:

$$P_L = \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100$$

Substitute the sums:

$$P_L = \frac{400}{320} \times 100$$ $$P_L = 1.25 \times 100$$ $$P_L = \boxed{\text{125.00}}$$

(ii) Paasche's method
The formula for Paasche's Price Index ($P_P$) is:

$$P_P = \frac{\sum p_1 q_1}{\sum p_0 q_1} \times 100$$

Substitute the sums:

$$P_P = \frac{260}{206} \times 100$$ $$P_P \approx 1.2621359 \times 100$$ $$P_P \approx \boxed{\text{126.21}}$$

*(iii) Bowley's