Question

The index number by the method of aggregates for the year 2010, taking 2000 as the base year, was found to be 116. If sum of the prices in the year 2000 is ₹ 300, find the values of x and y in the data given below

Commodity	A	B	C	D	E	F
Price in the year 2000 (₹)	50	x	30	70	116	20
Price in the year 2010 (₹)	60	24	y	80	120	28

Answer 1

	Base price (₹) in 2000 P0	Price(₹) in 2010 P1
A	50	60
B	x	24
C	30	y
D	70	80
E	116	120
F	20	28
	∑P0 = 286 + x	∑P1 = 312 + y

Given  ∑P₀  = 300

⇒ x = 300 - 286 = 14

Index number P₀₁ = 116

P₀₁ = `( ∑P_1)/( ∑P_0) xx 100`

116 = `(312 + y)/(300) xx 100`

⇒ 116 x 3 = 312 + y

⇒ y = 36

∴ x = 14, y = 36