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Standard X

Mathematics

Elimination Method of Finding Solution of a Pair of Linear Equations

The cost of ...

Question

The cost of $3 k g$ of rice and $4 k g$ of wheat is $R s . 93$ . The cost of $5 k g$ rice and $7 k g$ of wheat is $R s . 159$ . Find the prices of rice and wheat per $k g$ .

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Solution

Let the cost of $1$ kg of rice and wheat be $x$ & $y$ respectively.
given that $3 x + 4 y = 93$ -(i)
$5 x + 7 y = 159$ -(ii)
$(i) \times 5 - (i i) \times 3$
$- y = - 12 y = 12$
$3 a + 4 y = 93 3 x = 93 - 4 (12) = 93 - 48 = 45 x = 5$
$∴$ cost of rice $= 15$ Rs.
cost of wheat $= 12$ Rs. per kg

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The cost of 3 kg of rice and 4 kg of wheat is Rs. 93. The cost of 5 kg rice and 7 kg of wheat is Rs. 159. Find the prices of rice and wheat per kg.

Let the cost of 1 kg of rice and wheat be x & y respectively.given that 3x+4y=93 -(i)5x+7y=159 -(ii)(i)×5−(ii)×3−y=−12y=123a+4y=933x=93−4(12)=93−48=45x=5∴ cost of rice =15 Rs.cost of wheat =12Rs. per kg

The cost of $3 k g$ of rice and $4 k g$ of wheat is $R s . 93$ . The cost of $5 k g$ rice and $7 k g$ of wheat is $R s . 159$ . Find the prices of rice and wheat per $k g$ .

Let the cost of $1$ kg of rice and wheat be $x$ & $y$ respectively.
given that $3 x + 4 y = 93$ -(i)
$5 x + 7 y = 159$ -(ii)
$(i) \times 5 - (i i) \times 3$
$- y = - 12 y = 12$
$3 a + 4 y = 93 3 x = 93 - 4 (12) = 93 - 48 = 45 x = 5$
$∴$ cost of rice $= 15$ Rs.
cost of wheat $= 12$ Rs. per kg