Mathematics
The cost of 5 kg of sugar and 7 kg of rice is ₹153, and the cost of 7 kg of sugar and 5 kg of rice is ₹147. Find the cost of 6 kg of sugar and 10 kg of rice.
Linear Equations
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Answer
Let cost of sugar and rice per kg be ₹x and ₹y respectively.
So, cost of 5 kg of sugar and 7 kg of rice = 5x + 7y and,
cost of 7 kg of sugar and 5 kg of rice = 7x + 5y.
According to question,
5x + 7y = 153 …..(i)
7x + 5y = 147 ……(ii)
Multiplying eq (i) by 7 and eq (ii) by 5 we get,
35x + 49y = 1071 ……(iii)
35x + 25y = 735 ……(iv)
Subtracting (iv) from (iii) we get,
⇒ 35x + 49y - (35x + 25y) = 1071 - 735
⇒ 24y = 336
⇒ y = 14.
Substituting value of y in (i) we get,
⇒ 5x + 7(14) = 153
⇒ 5x + 98 = 153
⇒ 5x = 153 - 98
⇒ 5x = 55
⇒ x = 11.
∴ Cost of 6 kg of sugar and 10 kg of rice = 6x + 10y = 6(11) + 10(14) = 66 + 140 = ₹206.
Hence, cost of 6kg of sugar and 10 kg of rice = ₹206.
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