Question

Find the value of variables k and d for the following data using Simple aggregative method provided the average prices of commodities have increased by 50% over the given period.Also given is the relation between k and d defined by $k^2+d^2=149.$

$\begin{array}{cccccc}\text{Commodities}& A& B& C& D& E\\ \text{Price in 2000 (Rs.)}& 10& 12& 2& k& 23\\ \text{Price in 2006 (Rs.)}& 14& 17& d& 9& 31\end{array}$

• A. k = Rs. 7, d = Rs. 10
• B. k = Rs. 10, d = Rs. 10
• C. k = Rs. 7, d = Rs. 7
• D. k = Rs. 8, d = Rs. 5

Answer 1

The correct option is A

k = Rs. 7, d = Rs. 10

$k^2+d^2=149$ --------- (i)

$\begin{array}{ccccccc}\text{Commodities}& A& B& C& D& E& \text{Total}\\ \text{Price in 2000 (Rs.)}& 10& 12& 2& k& 23& 47+k\\ \text{Price in 2006 (Rs.)}& 14& 17& d& 9& 31& 71+d\end{array}$

Given, 71 + d = 1.5(47 + k)
142 + 2d = 141 + 3k
3k - 2d = 1 ------------ (ii)

Putting the value of d from (ii) into (i), we get
$k^2+[\frac{(3k-1)}{2}{]}^2=149$
$13k^2-6k-595=0$
k = Rs.7
Therefore , $d^2=149-7^2=149-49=100$
d = Rs.10