Question

In a class of $40$ students, $\frac{1}{5}$of the total number of students who like to study English, $\frac{2}{5}$of the total number like to study Mathematics and the remaining students like to study Science?

(I) How many students like to study English?

(ii) How many students like to study Mathematics?

(iii) What fraction of the total number of students like to study Science?

Answer 1

Step 1: Number of Students who like to study English

Given that, total number of students in the class $=40$

The number of students who like to study English $=\frac{1}{5}$of the total number of students

$=\frac{1}{5}$ of $40$

$$\begin{gathered} =\frac{1}{5}\times 40(\because Ofmeansmultiplication) \\ =\frac{40}{5} \\ =8 \end{gathered}$$

Hence, the number of students who like to study English $=8$

Step 2: Number of students who like to study Mathematics

The number of students who like to study Mathematics $=\frac{2}{5}$of the total number of students

$$\begin{gathered} =\frac{2}{5}of40 \\ =\frac{2}{5}\times 40(\because Ofmeansmultiplication) \\ =\frac{80}{5} \\ =16 \end{gathered}$$

Hence, the number of students who like to study Mathematics is $16$

Step 3: Fraction of students who like to study Science

Total Students $=$Students who like English $+$Students who like Mathematics $+$Students Who like Science

$\Rightarrow 40=8+16+$Students who like Science

$\Rightarrow 40=24+$Students who like Science

$\Rightarrow$Students who like Science$=40-24=16$

Now, the fraction of students who liked Science

$$\begin{gathered} =\frac{StudentswholikedScience}{TotalStudents} \\ =\frac{16}{40} \\ =\frac{2}{5} \end{gathered}$$

Hence, the fraction who like to study Science is $\frac{2}{5}$