# Solve the following

1. Calculate Price Index number from the given data:

 Commodity A B C D Price in 2005 (₹) 6 16 24 4 Price in 2010 (₹) 8 18 28 6

SOLUTION:-

 Commodity Price in 2005 (₹) P0 Price in 2010 (₹) P1 A 6 8 B 16 18 C 24 28 D 4 6 Total ∑P0 = 50 ∑P1 = 60

⇒ Here, ∑P0 = 50 and ∑P1 = 60
Using Simple Aggregate Price Index formula
∴ Simple Aggregate Price Index = P1/P0 * 100
= 60/50 * 100
=120

2. Calculate Quantity Index number from the given data:

 Commodity P Q R S T Base year quantities 170 150 100 195 205 Current year quantities 90 70 75 150 95

SOLUTION: –

 Commodity Base year quantities q0 Current year quantities q1 P 170 90 Q 150 70 R 100 75 S 195 150 T 205 95 Total ∑q0 = 820 ∑q1 = 480

Quantity Index Number = q1/q0 * 100
= 480/820 *100
= 58.54.

3. Calculate Value Index number from the given data:

 Commodity Base year Current year Price Quantity Price Quantity A 40 15 70 20 B 10 12 60 22 C 50 10 90 18 D 20 14 100 16 E 30 13 40 15

Solution: –

 Commodity Base year Current year p0 q0 p0q0 p1 q1 p1q1 A 40 15 600 70 20 1400 B 10 12 120 60 22 1320 C 50 10 500 90 18 1620 D 20 14 280 100 16 1600 E 30 13 390 40 15 600 Total ∑p0q0 = 1890 ∑p1q1 = 6540

value Index Number = p1q1/p0q0 * 100
= ∑p1q1/∑p0q0×100
= 6540/1890×100
= 346.03

4. A) Calculate Laaspeyre’s index from the given data:

 Commodity Base year current year Price Quantity Price Quantity X 8 30 12 25 Y 10 42 20 16

Solution: –

 Commodity Base year Current year p0 q0 p1 q1 p1q0 p0q0 X 8 30 12 25 360 240 Y 10 42 20 16 840 420 Total 1200 660

Laaspeyre’s index = p1q0/p0q0 * 100
= ∑p1q0/∑p0q0×100
= 1200/660×100
= 181.81

4. B Calculate Paasche’s index from the given data:

 Commodity Base year current year Price Quantity Price Quantity X 8 30 12 25 Y 10 42 20 16

Solution: –

 Commodity Base year Current year p0 q0 p1 q1 p1q1 p0q1 X 8 30 12 25 300 200 Y 10 42 20 16 320 160 Total 620 360

Paasche’s index = p1q1/p0q1
= ∑p1q1/∑p0q1×100
= 620/360×100
= 172.22