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

Correct option is (a) 15%

Let us take the complements of each given set.

n(H′) = 30%

n(E′) = 20%

n(E′ ∪ H′) = 100% − 65% = 35%

a + b = 35

a + 2b = 30 + 20 = 50

b = 15%