Question

In a class 65% students passed in maths, 50% passed in English
10% failed in both. If 40 students passed in both the subjects,
What is the total number students.​

Answer 1

Answer:

The total number of studens = 160

Step-by-step explanation:

If Set A denotes students passed in Maths and Set B denotes students passed in English and if total students are 100 then given

n(A) = 65

n(B) = 50

Students failed in both subject = 10

or, $n(\bar A \cap \bar B)=10$

or, $n(S)-n(A\cup B)=10$     (Remember De Morgan's Law for sets)

or, $100-n(A\cup B)=10$

or, $n(A\cup B)=90$

$n(A\cup B)=n(A)+n(B)-n(A\cap B)$

or, $90=65+50-n(A\cap B)$

or, $n(A\cap B) = 25$

Therefore, 25% students are passed in both the subjects

Let the number of students be x

then 25% of x = 40

or (25/100) × x = 40

or, x = 40 × 4 = 160