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A mixture of two grades of rice costs $20 per kg and $30 per kg. If the mixture

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Question: A mixture of two grades of rice costs $20 per kg and $30 per kg. If the mixture is sold at $25 per kg, what is the ratio of the two grades in the mixture?

Options:

  1. 1:1
  2. 1:2
  3. 2:1
  4. 3:2

Correct Answer: 1:2

Solution: 

Using alligation, (30-25)/(25-20) = 1/1. Ratio = 1:1.

A mixture of two grades of rice costs $20 per kg and $30 per kg. If the mixture

Practice Questions

Q1
A mixture of two grades of rice costs $20 per kg and $30 per kg. If the mixture is sold at $25 per kg, what is the ratio of the two grades in the mixture?
  1. 1:1
  2. 1:2
  3. 2:1
  4. 3:2

Questions & Step-by-Step Solutions

A mixture of two grades of rice costs $20 per kg and $30 per kg. If the mixture is sold at $25 per kg, what is the ratio of the two grades in the mixture?
  • Step 1: Identify the costs of the two grades of rice. One costs $20 per kg and the other costs $30 per kg.
  • Step 2: Identify the cost of the mixture, which is $25 per kg.
  • Step 3: Use the alligation method to find the ratio. Calculate the difference between the higher cost and the mixture cost: 30 - 25 = 5.
  • Step 4: Calculate the difference between the mixture cost and the lower cost: 25 - 20 = 5.
  • Step 5: Write the differences as a ratio: (30 - 25) : (25 - 20) = 5 : 5.
  • Step 6: Simplify the ratio 5:5 to 1:1.
  • Step 7: Conclude that the ratio of the two grades in the mixture is 1:1.
  • Alligation Method – A technique used to find the ratio of two or more ingredients in a mixture based on their costs and the cost of the mixture.
  • Weighted Average – Understanding how to calculate the average cost of a mixture based on the proportions of its components.
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