The cost of $2 k g$ of apples and $1 k g$ of grapes on a day was found to be $R s . 160$ . The cost of $4 k g$ of apples and $3 k g$ of grapes is $R s . 360$ . Find the cost of per kg apples and grapes.

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Solution

Let the cost of per $k g$ apples be $x$ and that of grapes be $y$ .
Case1:
The cost of $2 k g$ of apples and $1 k g$ of grapes on a day is $R s . 160$ .

$\Rightarrow 2 x + y = 160$ ---(1)
Case2:
The cost of $4 k g$ of apples and $3 k g$ of grapes is $R s . 360$

$\Rightarrow 4 x + 3 y = 360$ ---(2)
Lets solve (1) and (2),
Multiply the equation $2 x + y = 160$ by $2$ .
$\Rightarrow 4 x + 2 y = 320$ ---(3)
lets do (2)-(3),
$\Rightarrow 4 x + 3 y - (4 x + 2 y) = 360 - 320$
$\Rightarrow 4 x + 3 y - 4 x - 2 y) = 40$
$\Rightarrow y = 40$
Substitute, $y = 40$ in $2 x + y = 160$
$\Rightarrow 2 x + 40 = 160$
$\Rightarrow 2 x = 160 - 40$
$\Rightarrow 2 x = 120$
$\Rightarrow x = \frac{120}{2}$
$\Rightarrow x = 60$

Therefore, the cost of per $k g$ apples is $R s . 60$
cost of per $k g$ grapes is $R s . 40$ .

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