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 $x=y^3$.

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

• 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 1

The correct option is B

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

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

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

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