The prices and the quantities of three commodities are given are:

The Laspeyre's price index number for year 2009 with year 2006 as base is 200. The value of x is:

360

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 $360$.