In an examination, 56% of the candidates failed in English and 48% failed in science. If 18% failed in both English and science, find the percentage of those who passed in both the subjects.
Given:
In an examination:
- $56 \%$ of candidates failed in English
$-48 \%$ of candidates failed in science
- $18 \%$ of candidates failed in both English and Science
To Find;
Percentage of students who passed in both subjects.
Let us consider,
Percentage of candidates who failed in English $=n(E)=56$
Percentage of candidates who failed in Science $=n(S)=48$
Percentage of candidates who failed in English and Science both
$=n(E \cap S)=18$
Percentage of candidates who failed in English only $=n(E-S)$
Percentage of candidates who failed in Science only $=n(S-E)$
Venn diagram:
Now
$n(E-S)=n(E)-n(E \cap S)$
$=56-18$
$=38$
$n(S-E)=n(S)-n(E \cap S)$
$=48-18$
$=30$
Therefore,
Percentage of total candidates who failed =
$n(E-S)+n(S-E)+n(E \cap S)$
$=38+30+18=86 \%$
Now,
The percentage of candidates who passed in both English and
Science $=100-86=14 \%$
Hence
The percentage of candidates who passed in both English and
Science $=14 \%$