Question

In a school auditorium, ${\frac{1}{5}}^{\text{th}}$ of the students are fourth graders, ${\frac{1}{3}}^{\text{rd}}$ are fifth graders. Of the remaining students, ${\frac{1}{4}}^{\text{th}}$ of them are third graders, and the remaining are second graders. If the total number of students in the auditorium is 120, then what is the number of second graders in the auditorium?

Answer 1

Given that ${\frac{1}{5}}^{\text{th}}$ of the students are fourth graders, and ${\frac{1}{3}}^{\text{rd}}$ are fifth graders in the auditorium.
Since the total number of students equals 120,
the number of fourth graders is $\frac{1}{5}\times 120=24,$ and
the number of fifth graders is $\frac{1}{3}\times 120=40$
The remaining number of students is $120-(24+40)=56$
Now, the number of third graders is $\frac{1}{4}\times 56=14$
$⟹$ Number of second graders =$56-14=42$