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In a certain mixture, the ratio of two components is 2:3. If 5 liters of the fir

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Question: In a certain mixture, the ratio of two components is 2:3. If 5 liters of the first component is added, what will be the new ratio if the initial volume of the second component was 15 liters?

Options:

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

Correct Answer: 3:2

Solution: 

Let the initial amounts be 2x and 3x. After adding 5 liters to the first component, the new ratio becomes (2x + 5):3x. Solving gives 3:2.

In a certain mixture, the ratio of two components is 2:3. If 5 liters of the fir

Practice Questions

Q1
In a certain mixture, the ratio of two components is 2:3. If 5 liters of the first component is added, what will be the new ratio if the initial volume of the second component was 15 liters?
  1. 1:3
  2. 2:3
  3. 3:2
  4. 2:5

Questions & Step-by-Step Solutions

In a certain mixture, the ratio of two components is 2:3. If 5 liters of the first component is added, what will be the new ratio if the initial volume of the second component was 15 liters?
  • Step 1: Identify the initial ratio of the two components, which is 2:3.
  • Step 2: Let the initial amounts of the components be represented as 2x for the first component and 3x for the second component.
  • Step 3: Since the initial volume of the second component is given as 15 liters, we can set 3x = 15.
  • Step 4: Solve for x by dividing both sides of the equation by 3: x = 15 / 3 = 5.
  • Step 5: Now, calculate the initial amount of the first component: 2x = 2 * 5 = 10 liters.
  • Step 6: Add 5 liters to the first component: 10 liters + 5 liters = 15 liters.
  • Step 7: The amount of the second component remains the same at 15 liters.
  • Step 8: Now, we have 15 liters of the first component and 15 liters of the second component.
  • Step 9: Write the new ratio of the first component to the second component: 15:15.
  • Step 10: Simplify the ratio 15:15 to 1:1.
  • Ratios – Understanding and manipulating ratios to find new relationships between quantities.
  • Algebraic Representation – Using variables to represent quantities and solve for unknowns in a problem.
  • Mixture Problems – Applying concepts of mixtures and ratios to determine new proportions after changes.
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