You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Error and Uncertainty

The price rel...

Question

The price relatives and weight of a set commodities are given below:
Commodity A B C D
Price relative 125 120 127 119
Weight $x$ $2 x$ $y$ $y + 3$
If the sum of the weights is $40$ and weighted average of price relatives index number is $122$ , find the numerical values of $x$ and $y$ .

Open in App

Solution

Commodity Weight (w) Price relative (p) wp
A $x$ $125$ $125 x$
B $2 x$ $120$ $240 x$
x $y$ $127$ $127 y$
D $y + 3$ $119$ $119 y + 357$
Sum $3 x + 2 y + 3$ $356 x + 246 y + 357$
Sunm of weights $= 40$
$\Rightarrow 3 x + 2 y + 3 = 40$
$\Rightarrow 3 x + 2 y = 37$
Index number $= 122$
$\Rightarrow \frac{365 x + 246 y + 357}{40} = 122 \Rightarrow 365 x + 246 y = 4523...... (i i)$
Solving $(i)$ and $(i i)$
$\Rightarrow x = 7, y = 8$

Suggest Corrections

Similar questions

Q. The following commodities have the given price indices relative to a base of

100

. The weights are also given:

Commodity	Relative Index	Weight
Butter	181	4
Bread	116	12
Tea	110	3
Bacon	152	7

Calculate the new index for this set of commodities

The price quotation of different commodities for 2011 and 2012 are given below. Calculate the index number for 2012 with 2011 as base year by using (i) Simple average of price relative and (ii) Weighted average of price relative

Q. Calculate price index number by weighted average of price relative method.

Commodity	Price Base Year (in ₹)	Price current year ( in ₹)	Quantity Base year (in Kg)
A	6.0	8.0	40
B	3.0	3.2	80
C	2.0	3.0	2

Q. The average weight of three men

^{'} X^{'},^{'} Y^{'}

and

^{'} Z^{'}

75

kgs. Another mand

^{'} A^{'}

joins the group and the average weight now becomes

80 k g s

. If another person

^{'} B^{'}

whose weight is

5 k g s

more than

^{'} A

replaces

^{'} X^{'}

, then the average weight of

^{'} Y^{'},^{'} Z^{'},^{'} A^{'}

and

^{'} B^{'}

will be

85 k g s

. What is the weight of

^{'} X^{'}

Q. Calculate price index for the following data by applying weighted average of price relative method.

Item	Price in 1991 (Rs)	Price in 1992 (Rs)	Quantity in 1991
wheat	2.00	2.50	40 kg
sugar	3.00	3.25	20 kg
Milk	1.50	1.75	10 litre

Join BYJU'S Learning Program

Commodity	A	B	C	D
Price relative	125	120	127	119
Weight	$x$	$2 x$	$y$	$y + 3$

Commodity	Weight (w)	Price relative (p)	wp
A	$x$	$125$	$125 x$
B	$2 x$	$120$	$240 x$
x	$y$	$127$	$127 y$
D	$y + 3$	$119$	$119 y + 357$
Sum	$3 x + 2 y + 3$		$356 x + 246 y + 357$

The price relatives and weight of a set commodities are given below:CommodityABCDPrice relative125120127119Weightx2xyy+3If the sum of the weights is 40 and weighted average of price relatives index number is 122, find the numerical values of x and y.

Commodity Weight (w) Price relative (p) wp A x 125 125x B 2x 120 240x x y 127 127y D y+3 119 119y+357 Sum 3x+2y+3 356x+246y+357Sunm of weights =40⇒3x+2y+3=40⇒3x+2y=37Index number =122⇒365x+246y+35740=122⇒365x+246y=4523......(ii)Solving (i) and (ii)⇒x=7,y=8

The price relatives and weight of a set commodities are given below:
Commodity A B C D
Price relative 125 120 127 119
Weight $x$ $2 x$ $y$ $y + 3$
If the sum of the weights is $40$ and weighted average of price relatives index number is $122$ , find the numerical values of $x$ and $y$ .