Find the value of variables x and y for the following data using simple aggregative method provided the average prices of commodities have decreased by 25% over the given period. Also given is the relation between x and y defined by x = y 3 . Commodities A B C D E Price in 2000 (Rs.) 15 10 5 x 23 Price in 2006 (Rs.) 9 y 3 9 20 Options: A . &nbsp x and y are in the range of (0, 1) B . &nbsp x is in the range of (1,8) and y in (1,2) C . &nbsp x is the range of (8,27) and y in (2,3) D . &nbsp No such range exists for x and y

Answer: Option B : B x = y 3 --------- (i) Commodities A B C D E Total Price in 2000 (Rs.) 15 10 5 x 23 53 + x Price in 2006 (Rs.) 9 y 3 9 20 41 + y ( 3 4 ) ∗ ( 53 + x ) = ( 41 + y ) 159 + 3 x = 164 + 4 y 3x - 4y = 5 ------(ii) Putting the value of x from (i) into (ii), we get 3 y 3 − 4 y − 5 = 0 Clearly y lies in the range of (1, 2). Thus, x can lie in the range of (1, 8).

Find the value of variables x and y for the following data using simple aggreg

Question

Find the value of variables x and y for the following data using simple aggregative method provided the average prices of commodities have decreased by 25% over the given period. Also given is the relation between x and y defined by $x = y^{3}$ .

$\begin{matrix} Commodities & A & B & C & D & E Price in 2000 (Rs.) & 15 & 10 & 5 & x & 23 Price in 2006 (Rs.) & 9 & y & 3 & 9 & 20 \end{matrix}$

Options:

A . x and y are in the range of (0, 1)

B . x is in the range of (1,8) and y in (1,2)

C . x is the range of (8,27) and y in (2,3)

D . No such range exists for x and y

Answer: Option B
:
B

$x = y^{3}$ --------- (i)

$\begin{matrix} Commodities & A & B & C & D & E & Total Price in 2000 (Rs.) & 15 & 10 & 5 & x & 23 & 53 + x Price in 2006 (Rs.) & 9 & y & 3 & 9 & 20 & 41 + y \end{matrix}$

$(\frac{3}{4}) * (53 + x) = (41 + y) 159 + 3 x = 164 + 4 y$
3x - 4y = 5 ------(ii)
Putting the value of x from (i) into (ii), we get
$3 y^{3} - 4 y - 5 = 0$
Clearly y lies in the range of (1, 2).
Thus, x can lie in the range of (1, 8).