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To create a mixture that costs ₹110 per kg , 30 kg of one type of rice is combined with 60 kg of another type of rice that costs ₹100 per kg
Question

To create a mixture that costs ₹110 per kg , 30 kg of one type of rice is combined with 60 kg of another type of rice that costs ₹100 per kg.

A.

₹120 per kg

B.

₹125 per kg

C.

₹130 per kg

D.

₹135 per kg

Correct option is C

Given:
Quantity of Rice 1 = 30 kg
Cost of Rice 1 = Unknown (Let's call it 'x' ₹/kg)
Quantity of Rice 2 = 60 kg
Cost of Rice 2 = ₹100/kg
Cost of Mixture = ₹110/kg
Formula Used:
Cost of Mixture=Total Cost of Rice 1+Total Cost of Rice 2Total Quantity of Rice 1+Total Quantity of Rice 2\text{Cost of Mixture} = \frac{\text{Total Cost of Rice 1} + \text{Total Cost of Rice 2}}{\text{Total Quantity of Rice 1} + \text{Total Quantity of Rice 2}}​​
Solution:
Total cost of Rice 1 = 30 kg ×\times​ x ₹/kg = 30x ₹
Total cost of Rice 2 = 60 kg×\times₹100/kg = ₹6000
Total quantity = 30 kg + 60 kg = 90 kg
₹110/kg = (30x+6000)90kg\frac{(30x + ₹6000) }{ 90 \text{kg}}​​
110 ×\times​ 90 = 30x + 6000
9900 = 30x + 6000
3900 = 30x
x = 390030\frac{3900 }{30}​​
x = ₹130/kg
Therefore, the cost of the first type of rice is ₹130 per kg.

Thus, option (C) is right.

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