The cost of Type 1 material is Rs. 15 per kg and Type 2 material is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then what is the price per kg of the mixed variety of material?a)Rs. 19b)Rs. 16c)Rs. 18d)Rs. 17Correct answer is option 'C'. Can you explain this answer?

Question

Answer

C.)

Answer

Given:
Cost of Type 1 material = Rs. 15/kg
Cost of Type 2 material = Rs. 20/kg
Ratio of Type 1 and Type 2 material = 2:3

To find:
Price per kg of the mixed variety of material

Solution:
Let us assume that we have 2 kg of Type 1 material and 3 kg of Type 2 material. The total cost of this mixture would be:

Total cost = (2 kg x Rs.15/kg) + (3 kg x Rs.20/kg)
Total cost = Rs. 30 + Rs. 60
Total cost = Rs. 90

Therefore, the cost of 1 kg of the mixture would be Rs. 90/5 = Rs. 18/kg.

Hence, the price per kg of the mixed variety of material is Rs. 18/kg (Option C).

Alternatively, we can also solve this problem using weighted average formula:

Price per kg of the mixture = [(Price per kg of Type 1) x (Weight of Type 1) + (Price per kg of Type 2) x (Weight of Type 2)] / (Total weight)

Substituting the given values, we get:

Price per kg of the mixture = [(Rs. 15/kg) x 2 + (Rs. 20/kg) x 3] / (2+3)
Price per kg of the mixture = (Rs. 30 + Rs. 60) / 5
Price per kg of the mixture = Rs. 90/5
Price per kg of the mixture = Rs. 18/kg

Hence, the answer is Rs. 18/kg (Option C).

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