Question

While preparing the progress reports of the students, the class teacher found that $70$% of the students passed in Hindi, $80$% passed in English and only $65$% passed in both the subjects. Find out the percentage of students who failed in both the subjects

• A. $15$%
• B. $20$%
• C. $30$%
• D. $35$%

Answer 1

The correct option is A $15$%

Students passed in Hindi $=70\%=n\left(H\right)$

Students passed in English $=80\%=n\left(E\right)$

Students passed in Both $=65\%=n(H\cap E)$

No. of students passed $=n(H\cup E)=n\left(H\right)+n\left(E\right)-n(H\cap E)=70+80-65=85\%$

No. of Students failed $=100\%-n(H\cup E)=100\%-85\%=15\%$