In a class, $\frac{3}{5}$ of the students are girls and rest are boys. If $\frac{2}{9}$ of the girls and $\frac{1}{4}$ of the boys are absent, what part of the total number of students is present?
(a)$\frac{17}{25}$
(b)$\frac{18}{49}$
(c)$\frac{23}{30}$
(d)$\frac{23}{36}$
Answer
Answer (as printed): C
Explanation
Girls $=\frac{3}{5}$; Boys $=\left(1-\frac{3}{5}\right)=\frac{2}{5}$. Fraction of students absent $=\frac{2}{9}$ of $\frac{3}{5}+\frac{1}{4}$ of $\frac{2}{5}$ $$=\frac{6}{45}+\frac{1}{10}=\frac{21}{90}=\frac{7}{30} .$$ ∴ Fraction of students present $=\left(1-\frac{7}{30}\right)=\frac{23}{30}$.
Explanation as extracted from the printed page; notation may be imperfect.