Q. 164.6( 31 Votes )
The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs. 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs. 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs. 70. Find cost of each item per kg by matrix method.
Let the cost of onions, wheat and rice per kg be Rs. x, Rs. y and Rs. z respectively.
Then according to the giving situation, it can be represented by a system of equations as-
4x + 3y + 2z = 60
2x + 4y + 6z = 90
6x + 2y + 3z = 70
The system of equations can be written in the form of AX = B, where
Here |A| = 4(12-12)-3(6-36) + 2(4-24) = 50 ≠ 0
Hence A-1 will exist.
Now, A11 = 0, A12 = 30, A13 = -20, A21 = -5, A22 = 0, A23 = 10, A31 = 10, A32 = -20, A33 = 10
Hence x = 5, y = 8 & z = 8.
Hence, the cost of onions is Rs. 5 per kg, the cost of wheat is Rs. 8 per kg, and the cost of rice is Rs. 8 per kg
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