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In a mixture of two liquids, the ratio of liquid X to liquid Y is 1:3. If 12 lit

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Question: In a mixture of two liquids, the ratio of liquid X to liquid Y is 1:3. If 12 liters of liquid Y is added, what will be the new ratio if the total volume is 48 liters?

Options:

  1. 1:2
  2. 1:3
  3. 1:4
  4. 1:5

Correct Answer: 1:4

Solution: 

Let the volumes of X and Y be x and 3x. x + 3x + 12 = 48. Solving gives x = 6. New ratio = 6:18 = 1:3.

In a mixture of two liquids, the ratio of liquid X to liquid Y is 1:3. If 12 lit

Practice Questions

Q1
In a mixture of two liquids, the ratio of liquid X to liquid Y is 1:3. If 12 liters of liquid Y is added, what will be the new ratio if the total volume is 48 liters?
  1. 1:2
  2. 1:3
  3. 1:4
  4. 1:5

Questions & Step-by-Step Solutions

In a mixture of two liquids, the ratio of liquid X to liquid Y is 1:3. If 12 liters of liquid Y is added, what will be the new ratio if the total volume is 48 liters?
  • Step 1: Understand the initial ratio of liquid X to liquid Y, which is 1:3. This means for every 1 part of liquid X, there are 3 parts of liquid Y.
  • Step 2: Let the volume of liquid X be represented as 'x'. Since the ratio is 1:3, the volume of liquid Y will be '3x'.
  • Step 3: Write the equation for the total volume of the mixture. The total volume is the sum of liquid X and liquid Y plus the additional liquid Y added: x + 3x + 12 = 48.
  • Step 4: Simplify the equation. Combine like terms: 4x + 12 = 48.
  • Step 5: Solve for 'x'. Subtract 12 from both sides: 4x = 36. Then divide by 4: x = 9.
  • Step 6: Calculate the volumes of liquid X and Y. Liquid X is 9 liters, and liquid Y is 3 times that, which is 3 * 9 = 27 liters.
  • Step 7: Add the 12 liters of liquid Y that was added to the original volume of liquid Y: 27 + 12 = 39 liters.
  • Step 8: Now, the new volumes are liquid X = 9 liters and liquid Y = 39 liters.
  • Step 9: Find the new ratio of liquid X to liquid Y: 9:39.
  • Step 10: Simplify the ratio 9:39 by dividing both numbers by 9: 1:4.
  • Ratios – Understanding and manipulating ratios of quantities in a mixture.
  • Algebraic Equations – Setting up and solving equations based on given conditions.
  • Volume Calculation – Calculating total volume and adjusting for added quantities.
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