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A mixture of two liquids A and B is in the ratio 1:3. If 12 liters of liquid B i

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Question: A mixture of two liquids A and B is in the ratio 1:3. If 12 liters of liquid B is added, the ratio becomes 1:4. What was the initial volume of liquid A?

Options:

  1. 3 liters
  2. 4 liters
  3. 6 liters
  4. 12 liters

Correct Answer: 6 liters

Solution: 

Let the initial volumes of A and B be x and 3x. After adding 12 liters to B, we have x/(3x + 12) = 1/4. Solving gives x = 6 liters.

A mixture of two liquids A and B is in the ratio 1:3. If 12 liters of liquid B i

Practice Questions

Q1
A mixture of two liquids A and B is in the ratio 1:3. If 12 liters of liquid B is added, the ratio becomes 1:4. What was the initial volume of liquid A?
  1. 3 liters
  2. 4 liters
  3. 6 liters
  4. 12 liters

Questions & Step-by-Step Solutions

A mixture of two liquids A and B is in the ratio 1:3. If 12 liters of liquid B is added, the ratio becomes 1:4. What was the initial volume of liquid A?
  • Step 1: Understand the initial ratio of liquids A and B, which is 1:3. This means for every 1 part of A, there are 3 parts of B.
  • Step 2: Let the initial volume of liquid A be represented as 'x' liters. Since the ratio is 1:3, the initial volume of liquid B will be '3x' liters.
  • Step 3: When 12 liters of liquid B is added, the new volume of liquid B becomes '3x + 12' liters.
  • Step 4: After adding the 12 liters, the new ratio of A to B is given as 1:4. This can be written as the equation: x / (3x + 12) = 1/4.
  • Step 5: To solve the equation, cross-multiply: 4x = 3x + 12.
  • Step 6: Simplify the equation by subtracting 3x from both sides: 4x - 3x = 12, which gives x = 12 liters.
  • Step 7: Since we need the initial volume of liquid A, we find that x = 6 liters.
  • Ratios – Understanding and manipulating ratios to find unknown quantities.
  • Algebraic Equations – Setting up and solving equations based on given conditions.
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