Question

In an examination ,50% students failed in English,40% failed in math and 15% students failed in both subject .if 200 students passed in both subject then find the no of students appear in the exam​

Answer 1

Answer:  The required number of students that appear in the exam is 800.

Step-by-step explanation:  Given that in an examination, 50% students failed in English, 40% failed in math and 15% students failed in both subject.

Also, 200 students passed in both subject.

We are to find the number of students that passed in both he subjects.

Let x represents the total number of students in the class. Also, let A and B represents the set of students who failed in English and Math respectively.

Then, according to the given information, we have

$n(A)=50\%\times x=\dfrac{50}{100}\times x=\dfrac{x}{2},\\\\\\n(B)=40\%\times x=\dfrac{40}{100}\times x=\dfrac{2x}{5},\\\\\\n(A\cap B)=15\%\times x=\dfrac{15}{100}\times x=\dfrac{3x}{20}.$

From set theory, we have

$n(A\cup B)=n(A)+n(B)-n(A\cap B)\\\\\Rightarrow n(A\cup B)=\dfrac{x}{2}+\dfrac{2x}{5}-\dfrac{3x}{20}\\\\\\\Rightarrow n(A\cup B)=\dfrac{10x+8x-3x}{20}\\\\\\\Rightarrow n(A\cup B)=\dfrac{15x}{20}\\\\\\\Rightarrow n(A\cup B)=\dfrac{3x}{4}.$

So, the number of students of students who passed in either of the subjects is $\dfrac{3x}{4}.$

Therefore, the number of students who passed in both the subjects is given by

$x-\dfrac{3x}{4}=200\\\\\\\Rightarrow \dfrac{x}{4}=200\\\\\Rightarrow x=4\times200\\\\\Rightarrow x=800.$

Thus, the required number of students that appear in the exam is 800.