Question

In examination, {\text{42% }}students failed in mathematics and {\text{52% }}failed in science. If {\text{17% }}failed in both the subjects. Find the percentage who passed in both the subjects?

Answer 1

First let us calculate individual failing of the students in both the subjects from there we can use the logic that
{\text{ = 100% - (fail% )}}, and on using above equation we can obtain our required answer.

Complete step by step answer:

As given that {\text{17% }}failed in both the subjects, and {\text{42% }}students failed in mathematics and {\text{52% }}failed in science.
The number of students that only failed in mathematics{\text{ = 42 - 17 = 25% }}
The number of students that only failed in science{\text{ = 52 - 17 = 35% }}
And so the total numbers of failed students only in maths, only in science and both maths and science are

{\text{ = 35 + 25 + 17% }} \\\ {\text{ = 77% }} \\\

Hence, students passed in both the subjects are

{\text{ = 100% - (fail% )}} \\\ {\text{ = 100 - (77)% }} \\\ {\text{ = 23% }} \\\

Hence, there are 23% of students who passed in both subjects.

Note: We can also proceed with the question using the Venn-diagram method, A Venn diagram also called the primary diagram, set diagram, or logic diagram, is a diagram that shows all possible logical relations between a finite collection of different sets. These diagrams depict elements as points in the plane and sets as regions inside closed curves.