Question

In a school there are 100 students. One-fifth of the students in the school are boys, out of these boys one-fourth are studying in lower grades and the remaining are studying in higher grades. What is the fraction of boys studying in upper classes when compared to the entire school?

• A. $\frac{3}{35}$
• B. $\frac{3}{20}$
• C. $\frac{30}{35}$
• D. $\frac{6}{30}$

Answer 1

The correct option is B $\frac{3}{20}$

Fraction of boys studying in school = $\frac{1}{5}$
So, the total number of boys in the school is equal to
$\frac{1}{5}\times 100=20$

Now, out of these 20 boys in the entire school, only one-fourth or $\frac{1}{4}$ are in lower grades.
Hence, the total number of boys studying in lower grades is equal to
$\frac{1}{4}\times 20=5$

The total number of boys in the higher grades in equal to $20-5=15$

So, now we can calculate the fraction of boys studying in the higher grades with respect to the entire school.

$Fraction=\frac{Numberofboysinhighergrades}{Totalnumberofstudents}$

$Fraction=\frac{15}{100}=\frac{3}{20}$.

So, the answer is $\frac{3}{20}$.