Solve both mixture math problems.
Understand the Problem
The image contains two mixture problems. One involves the mixture of two types of rice with different prices to determine the quantity ratio. The other deals with students taking an exam, where the percentages of boys and girls qualifying are given, and asks questions about the overall percentage of qualified students.
Answer
The required ratio is $3:7$.
Answer for screen readers
The two mixtures must be mixed in the ratio $3:7$.
Steps to Solve
- Correct typo from OCR
The OCR has some mistakes. The problem statement should read: "In what ratio must a mixture of 30% alcohol strength be mixed with that of 80% alcohol strength so as to get a mixture of 45% alcohol strength?"
- Set up the Alligation method
We use the alligation method to find the ratio in which the two mixtures should be mixed. Alligation is a simplified approach to mixture problems, based on the weighted average concept.
- Apply the alligation rule
Place the percentage of the mixture in the middle and the percentages of the two ingredients at the two corners. Subtract diagonally and find the difference.
- Calculate the differences
Difference 1 = 80 - 45 = 35 Difference 2 = 45 - 30 = 15
- Determine the ratio
The ratio is the two differences written as a fraction: Ratio = Difference 2 : Difference 1 = 15 : 35
- Simplify the ratio
Divide both sides of the ratio by their greatest common divisor, which is 5. $15 \div 5 = 3$ $35 \div 5 = 7$
Therefore, the simplified ratio is 3 : 7.
The two mixtures must be mixed in the ratio $3:7$.
More Information
The alligation method provides a quick way to solve mixture problems, which are commonly encountered in quantitative aptitude tests. It simplifies the weighted average calculation involved in mixing different quantities.
Tips
A common mistake is to subtract in the wrong order, leading to a negative ratio. Always subtract the smaller value from the larger one to ensure a positive ratio. Another common mistake is forgetting to simplify the final ratio.
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