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In a mixture of three types of fruit juices, the ratio of juice A to juice B is

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Question: In a mixture of three types of fruit juices, the ratio of juice A to juice B is 1:2, and the ratio of juice B to juice C is 3:4. What is the ratio of juice A to juice C?

Options:

  1. 1:6
  2. 2:3
  3. 3:4
  4. 1:8

Correct Answer: 1:6

Solution: 

Let A = x, B = 2x, C = (4/3) * 2x = (8/3)x. Thus, A:C = x:(8/3)x = 1:8.

In a mixture of three types of fruit juices, the ratio of juice A to juice B is

Practice Questions

Q1
In a mixture of three types of fruit juices, the ratio of juice A to juice B is 1:2, and the ratio of juice B to juice C is 3:4. What is the ratio of juice A to juice C?
  1. 1:6
  2. 2:3
  3. 3:4
  4. 1:8

Questions & Step-by-Step Solutions

In a mixture of three types of fruit juices, the ratio of juice A to juice B is 1:2, and the ratio of juice B to juice C is 3:4. What is the ratio of juice A to juice C?
  • Step 1: Understand the given ratios. The ratio of juice A to juice B is 1:2. This means for every 1 part of juice A, there are 2 parts of juice B.
  • Step 2: Assign a variable to juice A. Let juice A be represented as 'x'.
  • Step 3: Use the ratio to find juice B. Since the ratio of A to B is 1:2, if A = x, then B = 2x.
  • Step 4: Now, look at the second ratio given, which is the ratio of juice B to juice C, which is 3:4. This means for every 3 parts of juice B, there are 4 parts of juice C.
  • Step 5: Since we have B = 2x, we can set up the ratio. If B = 2x corresponds to 3 parts, we can find C. Let C = (4/3) * B = (4/3) * (2x).
  • Step 6: Calculate C. C = (4/3) * (2x) = (8/3)x.
  • Step 7: Now we have A = x, B = 2x, and C = (8/3)x. We need to find the ratio of A to C.
  • Step 8: Set up the ratio A:C. This is x : (8/3)x.
  • Step 9: Simplify the ratio. The x's cancel out, giving us 1 : (8/3).
  • Step 10: To express this in a simpler form, multiply both sides by 3 to eliminate the fraction: 1 * 3 : (8/3) * 3, which gives us 3 : 8.
  • Step 11: Therefore, the final ratio of juice A to juice C is 1:8.
  • Ratios – Understanding and manipulating ratios to find relationships between different quantities.
  • Proportions – Using proportions to relate different parts of a mixture.
  • Algebraic Manipulation – Applying algebra to express relationships and solve for unknowns.
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