Class 10MathematicsPair of Linear Equations in Two VariablesMix Examples - Pair of Linear Equations in Two Variables
MediumThe 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 $4x + 2y = 300$.
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 $4x + 2y = 300$.
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Similar Questions
Which of the following groups truly matches the data of Part $I$ with the data of Part $II$?
Part $I$ Part $II$ $1.$ The solution of $2x - y = 4$ and $3x - 2y = 5$ $a.$ $x = 3, y = 2$ $2.$ The solution of $5x - y = 14$ and $4x - 3y = 9$ $b.$ $x = 3, y = 1$ $3.$ The solution of $4x - 3y = 5$ and $3x - y = 5$ $c.$ $x = 2, y = 1$ $4.$ The solution of $3x - 2y = -1$ and $2x - 5y = -8$ $d.$ $x = 1, y = 2$
| Part $I$ | Part $II$ |
| $1.$ The solution of $2x - y = 4$ and $3x - 2y = 5$ | $a.$ $x = 3, y = 2$ |
| $2.$ The solution of $5x - y = 14$ and $4x - 3y = 9$ | $b.$ $x = 3, y = 1$ |
| $3.$ The solution of $4x - 3y = 5$ and $3x - y = 5$ | $c.$ $x = 2, y = 1$ |
| $4.$ The solution of $3x - 2y = -1$ and $2x - 5y = -8$ | $d.$ $x = 1, y = 2$ |
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