Practice With Solutions: Alligation Alternate For Mixing Concentrations

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Alligation alternate is a useful mathematical technique used to mix solutions of different concentrations to achieve a desired concentration. It simplifies complex calculations and helps in practical scenarios such as pharmacy, chemistry, and manufacturing. This article provides practice problems with solutions to master the alligation alternate method.

Understanding Alligation Alternate Method

The alligation alternate method involves balancing the parts of solutions with different concentrations to obtain a mixture of a specific concentration. It is especially helpful when mixing two solutions of different strengths to get a desired concentration.

Practice Problem 1

Mix 40% and 60% solutions to get 50% solution. Find the ratio in which they should be mixed.

Solution

Difference between the given concentrations and the desired concentration:

  • For 40%: 50 – 40 = 10
  • For 60%: 60 – 50 = 10

Ratio of solutions = 10 : 10 = 1 : 1

Hence, equal parts of 40% and 60% solutions should be mixed to get 50% solution.

Practice Problem 2

Mix 20% and 80% solutions to obtain 50% solution. Find the ratio in which they should be mixed.

Solution

Calculate the differences:

  • For 20%: 50 – 20 = 30
  • For 80%: 80 – 50 = 30

Ratio of solutions = 30 : 30 = 1 : 1

Equal parts of 20% and 80% solutions are needed to make a 50% solution.

Practice Problem 3

Mix 10% and 30% solutions to obtain 20% solution. Find the ratio in which they should be mixed.

Solution

Differences are:

  • For 10%: 20 – 10 = 10
  • For 30%: 30 – 20 = 10

Ratio = 10 : 10 = 1 : 1

Equal parts of 10% and 30% solutions should be mixed to get 20% solution.

Additional Practice

Try solving these problems using the alligation alternate method to strengthen your understanding:

  • Mix 25% and 75% solutions to get 50%. Find the ratio.
  • Mix 15% and 45% solutions to get 30%. Find the ratio.
  • Mix 5% and 95% solutions to get 50%. Find the ratio.

Conclusion

The alligation alternate method provides a quick and efficient way to solve mixture problems involving different concentrations. Practice regularly with various problems to develop confidence and accuracy in your calculations.