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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 Verified Verified
Hint: 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.