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
Answer (as printed): A
Explanation
$n(\mathrm{A})=34, n(\mathrm{B})=42, n(\mathrm{A} \cap \mathrm{B})=20$. So, $n(\mathrm{A} \cup \mathrm{B})=n(\mathrm{A})+n(\mathrm{B})-n(\mathrm{A} \cap \mathrm{B})$ $$=34+42-20=56 .$$ ∴ Percentage failed in either or both the subjects = 56. Hence, percentage passed $=(100-56) \%=44 \%$.