In a class, \( \frac{5}{9} \) of the students are girls and the rest are boys. If \( \frac{1}{4} \) of the girls and \( \frac{2}{3} \) of the boys are absent, and the total number of students present is 245 (taking 244 for calculation), what is the total number of students in the class?

Explanation

Let the total number of students be \( x \). Number of girls = \( \frac{5}{9}x \) and number of boys = \( (1 - \frac{5}{9})x = \frac{4}{9}x \). Girls present = \( (1 - \frac{1}{4}) \times \frac{5}{9}x = \frac{3}{4} \times \frac{5}{9}x = \frac{5}{12}x \). Boys present = \( (1 - \frac{2}{3}) \times \frac{4}{9}x = \frac{1}{3} \times \frac{4}{9}x = \frac{4}{27}x \). According to the question, total students present = \( \frac{5}{12}x + \frac{4}{27}x = 244 \) (using 244 for a whole number result instead of 245). \( \frac{45 + 16}{108}x = 244 \) or \( \frac{61}{108}x = 244 \). \( x = \frac{244 \times 108}{61} = 4 \times 108 = 432 \).