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 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 cost of each Kg of onion = Rs x

Cost of each Kg of wheat  = Rs y

And cost of each Kg of rice = Rs z

Given that cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60

So

                        4x + 3y + 2 z = 60                 …(1)

Given that The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs 90

So

2x + 4y + 6z = 90     

Divide equation by 2 we get

X + 2y + 3z = 45                    … (2)

Given that The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs 70.

So

                        6x + 2y + 3z = 70                  … (3)

So our set of equation is

4x + 3y + 2 z = 60

2x + 4y + 6z = 90

6x + 2y + 3z = 70

Use formula

Plug the value we get

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ð  Take 5 common there we get

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ð  Price of onion x =Rs 5 / Kg

ð  Price of wheat y=8 Rs/Kg  

ð  Price of rice z = 8 Rs/Kg