The cost of $2\, kg$ of apples and $1\, kg$ of grapes on a day was found to be ₹ $160$. After a month,the cost of $4\, kg$ of apples and $2\, kg$ of grapes is ₹ $300$. Represent the situation algebraically and geometrically.

(N/A) Let the cost of $1\, kg$ of apples be ₹ $x$ and the cost of $1\, kg$ of grapes be ₹ $y$.
According to the question,the algebraic representation is:
$2x + y = 160$
$4x + 2y = 300$
For the equation $2x + y = 160$,we have $y = 160 - 2x$. The solution table is:

$x$	$50$	$60$	$70$
$y$	$60$	$40$	$20$

For the equation $4x + 2y = 300$,we have $y = \frac{300 - 4x}{2} = 150 - 2x$. The solution table is:

$x$	$70$	$80$	$75$
$y$	$10$	$-10$	$0$

The graphical representation shows two parallel lines,indicating that the system has no solution.