In a class, 20% of the boys have blue eyes and 10% of the girls have blue eyes. If the ratio of boys to girls in the class is 4:3, then what is the portion of the students in the class having blue eyes?
$\frac{11}{70}$
To find the portion of students in the class with blue eyes, we first need to consider the given parameters and calculate step by step:
- Understanding the ratio of boys to girls:
- The ratio of boys to girls is given as 4:3. This implies that for every 7 students, 4 are boys and 3 are girls.
- Percentage of boys with blue eyes:
- According to the problem, 20% of the boys have blue eyes.
- Percentage of girls with blue eyes:
- 10% of the girls have blue eyes.
- Assuming total students as a multiple of 7:
- Assume there are 7*k students in the class (k being some integer) for simplicity of calculation.
- Then, number of boys = \(4k\) and number of girls = \(3k\).
- Finding students with blue eyes:
- Boys with blue eyes = \(0.2 \times 4k = 0.8k\).
- Girls with blue eyes = \(0.1 \times 3k = 0.3k\).
- Total students with blue eyes = \(0.8k + 0.3k = 1.1k\).
- Calculate the required portion:
- Total number of students = \(7k\).
- Portion of students with blue eyes = \(\frac{1.1k}{7k} = \frac{11}{70}\).
Therefore, the portion of the students in the class having blue eyes is \(\frac{11}{70}\), which matches with option 11/70.
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