In an examination, 34% of the students failed in Mathematics and 42% failed in English. If 20% of the students failed in both the subjects, then the percentage of students who passed in both the subjects was :

A. 44%

B. 50%

C. 54%

D. 56%

Answer: Option D

Solution(By Examveda Team)

$$\eqalign{ & n\left( A \right) = 34 \cr & n\left( B \right) = 42 \cr & n\left( {A \cap B} \right) = 20 \cr & {\text{So, }} \cr & {\text{n}}\left( {A \cup B} \right) \cr & = n\left( A \right) + n\left( B \right) - n\left( {A \cap B} \right) \cr & = 34 + 42 - 20 \cr & = 56 \cr} $$
∴ Percentage failed in either or both the subjects = 56%