If $6$ kg of sugar and $5$ kg of tea together cost Rs. $209$ and $4$ kg of sugar and $3$ kg of tea together cost Rs. $131$, then the cost of $1$ kg sugar and $1$ kg tea are respectively

The correct option is A Rs. $14$ and Rs. $25$
Let the price of sugar be $x$ and tea be $y$.
Then,

$6x+5y=\mathrm{209....}\left(1\right)$
$4x+3y=\mathrm{131....}\left(2\right)$
Multiply equation $\left(1\right)$ by $4$ and equation $\left(2\right)$ by $6$ and then subtract:

$(6x+5y=209)4$

$(4x+3y=131)6$

$.............................................$

$24x+20y-24x-18y=209\times 4-131\times 6$
$.............................................$
$2y=836-786$
$2y=50$
$y=25$
Therefore, $x=14$
Price of sugar is $Rs.14$ and price of tea is $Rs.25$ .