The prices and the quantities of three commodities are given are:
|
Commodity |
Price (₹) |
Quantities |
||
|
in Year 2006 |
in Year 2009 |
in Year 2006 |
in Year 2009 |
|
|
P |
100 |
90 |
12 |
10 |
|
Q |
80 |
x |
8 |
7 |
|
R |
60 |
50 |
4 |
6 |
The Laspeyre's price index number for year 2009 with year 2006 as base is 200. The value of x is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) - 360
$\text{Laspeyres index } P_{01} = \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100 = 200$
$\sum p_1 q_0 = 90\cdot12 + x\cdot8 + 50\cdot4$
$= 1080 + 8x + 200 = 1280 + 8x$
$\sum p_0 q_0 = 100\cdot12 + 80\cdot8 + 60\cdot4$
$= 1200 + 640 + 240 = 2080$
$\frac{1280 + 8x}{2080} \times 100 = 200$
$\frac{1280 + 8x}{2080} = 2$
$1280 + 8x = 4160$
$8x = 2880$
$x = 360$
The value of $x$ is $360$.