The cost of $2\,kg$ of apples and $1\,kg$ of grapes on a day was found to be Rs. $160$. After a month,the cost of $4\,kg$ of apples and $2\,kg$ of grapes is Rs. $300$. Represent this situation as a pair of linear equations in two variables.

(N/A) Let the cost of $1\,kg$ of apples be Rs. $x$ and the cost of $1\,kg$ of grapes be Rs. $y$.
According to the first condition,the total cost of $2\,kg$ of apples and $1\,kg$ of grapes is Rs. $160$.
Therefore,the equation is: $2x + y = 160$ $... (1)$
According to the second condition,the total cost of $4\,kg$ of apples and $2\,kg$ of grapes is Rs. $300$.
Therefore,the equation is: $4x + 2y = 300$ $... (2)$
Thus,the pair of linear equations in two variables representing the given situation is $2x + y = 160$ and $4x + 2y = 300$.