Question

In a class, each student likes either mathematics or science or both. The number of students who like mathematics and science are 248 and 200, respectively.
One-fourth of the students who like mathematics also like science. Find the total number of students in the class.

Answer 1

Number of students who like mathematics = 248
Number of students who like science = 200

The number of students who like both mathematics and science is one-fourth the number of students who like mathematics.

Thus,
$\text{Number of students who like both subjects}$
$=\frac{1}{4}\times 248=62$

Number of students who only like mathematics = 248 – 62 = 186

Number of students who only like science = 200 – 62 = 138

So, showing the number of students in a Venn diagram, we get:


So, total number of students in the class = 186 + 62 + 138 = 386

Thus, there are 386 students in the class.