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A mixture of two liquids A and B is in the ratio 4:5. If 9 liters of liquid B is

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Question: A mixture of two liquids A and B is in the ratio 4:5. If 9 liters of liquid B is added, the ratio becomes 4:6. What was the initial quantity of liquid B?

Options:

  1. 18 liters
  2. 20 liters
  3. 22 liters
  4. 24 liters

Correct Answer: 20 liters

Solution: 

Let the initial quantities be 4x and 5x. After adding 9 liters of B, the new ratio is (4x)/(5x + 9) = 4/6. Solving gives x = 3, so initial quantity of B = 5x = 15 liters.

A mixture of two liquids A and B is in the ratio 4:5. If 9 liters of liquid B is

Practice Questions

Q1
A mixture of two liquids A and B is in the ratio 4:5. If 9 liters of liquid B is added, the ratio becomes 4:6. What was the initial quantity of liquid B?
  1. 18 liters
  2. 20 liters
  3. 22 liters
  4. 24 liters

Questions & Step-by-Step Solutions

A mixture of two liquids A and B is in the ratio 4:5. If 9 liters of liquid B is added, the ratio becomes 4:6. What was the initial quantity of liquid B?
  • Step 1: Understand the initial ratio of liquids A and B, which is 4:5. This means for every 4 parts of A, there are 5 parts of B.
  • Step 2: Let the initial quantities of A and B be represented as 4x and 5x, where x is a common multiplier.
  • Step 3: When 9 liters of liquid B is added, the new quantity of B becomes (5x + 9).
  • Step 4: The new ratio of A to B is given as 4:6. We can write this as (4x)/(5x + 9) = 4/6.
  • Step 5: Cross-multiply to eliminate the fraction: 4x * 6 = 4 * (5x + 9).
  • Step 6: Simplify the equation: 24x = 20x + 36.
  • Step 7: Solve for x by subtracting 20x from both sides: 24x - 20x = 36, which gives 4x = 36.
  • Step 8: Divide both sides by 4 to find x: x = 9.
  • Step 9: Now, find the initial quantity of liquid B by calculating 5x: 5 * 9 = 45 liters.
  • Ratios and Proportions – Understanding how to set up and manipulate ratios to find unknown quantities.
  • Algebraic Manipulation – Using algebra to solve equations derived from the problem statement.
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