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Class Z has 50% more students than class Y. Number of girls in class Y is equal to number of boys in class Z. The percentage of girls is the same in both classes. What percentage of the student group are boys?

Question

Class Z has 50% more students than class Y. Number of girls in class Y is equal to number of boys in class Z. The percentage of girls is the same in both classes. What percentage of the student group are boys?

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Solution

Let's break down the problem step by step:

  1. Let's assume the number of students in class Y is 100 (we choose 100 because it's easy to work with percentages).

  2. According to the problem, class Z has 50% more students than class Y. So, class Z has 150 students.

  3. The number of girls in class Y is equal to the number of boys in class Z. We don't know this number yet, but we know that the percentage of girls is the same in both classes.

  4. Let's denote the percentage of girls by x. So, in class Y, there are 100x girls and in class Z, there are 150x girls.

  5. But we know that the number of girls in class Y is equal to the number of boys in class Z. So, 100x = 150 - 150x. Solving this equation for x, we get x = 60/100 = 0.6 or 60%.

  6. Therefore, the percentage of girls in both classes is 60%. Since the total percentage is always 100%, the percentage of boys is 100% - 60% = 40%.

This problem has been solved

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