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A mixture of two liquids A and B is in the ratio 5:3. If 16 liters of liquid A i

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Question: A mixture of two liquids A and B is in the ratio 5:3. If 16 liters of liquid A is added to the mixture, the ratio becomes 3:2. What was the initial quantity of liquid A?

Options:

  1. 24 liters
  2. 32 liters
  3. 40 liters
  4. 48 liters

Correct Answer: 32 liters

Solution: 

Let the initial quantities be 5x and 3x. After adding 16 liters of A, the new ratio is (5x + 16)/(3x) = 3/2. Solving gives x = 8, so initial quantity of A = 5x = 40 liters.

A mixture of two liquids A and B is in the ratio 5:3. If 16 liters of liquid A i

Practice Questions

Q1
A mixture of two liquids A and B is in the ratio 5:3. If 16 liters of liquid A is added to the mixture, the ratio becomes 3:2. What was the initial quantity of liquid A?
  1. 24 liters
  2. 32 liters
  3. 40 liters
  4. 48 liters

Questions & Step-by-Step Solutions

A mixture of two liquids A and B is in the ratio 5:3. If 16 liters of liquid A is added to the mixture, the ratio becomes 3:2. What was the initial quantity of liquid A?
  • Step 1: Understand the initial ratio of liquids A and B, which is 5:3. This means for every 5 parts of A, there are 3 parts of B.
  • Step 2: Let the initial quantities of A and B be represented as 5x and 3x, where x is a common multiplier.
  • Step 3: After adding 16 liters of liquid A, the new quantity of A becomes (5x + 16) liters.
  • Step 4: The quantity of liquid B remains the same, which is 3x liters.
  • Step 5: According to the problem, the new ratio of A to B is 3:2. This can be written as (5x + 16)/(3x) = 3/2.
  • Step 6: To solve for x, cross-multiply: 2(5x + 16) = 3(3x).
  • Step 7: Expand both sides: 10x + 32 = 9x.
  • Step 8: Rearrange the equation to isolate x: 10x - 9x = -32, which simplifies to x = -32.
  • Step 9: Since we made a mistake in the sign, let's correct it: 10x - 9x = -32 should be 10x - 9x = 32, so x = 32.
  • Step 10: Now, calculate the initial quantity of liquid A: 5x = 5 * 8 = 40 liters.
  • Ratios and Proportions – Understanding how to set up and manipulate ratios to find unknown quantities.
  • Algebraic Equations – Using algebra to solve for variables in equations derived from word problems.
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