Question

In an examination 80% of the students passed by in English 85% in mathematics and 75% in both English and mathematics if 40 students fail in both the subjects are found the total number of students​

Answer 1

Let the -

• total number of students be x

→ 80% students passed in English examination.

$\rightarrow\:\sf{\dfrac{80}{100}\:\times\:x}$

$\rightarrow\:\sf{\dfrac{4x}{5}}$ ...(1)

→ 85% students passed in mathematics examination.

$\rightarrow\:\sf{\dfrac{85}{100}\:\times\:x}$

$\rightarrow\:\sf{\dfrac{17x}{20}}$ ...(2)

→ 75% students passed in both english and mathematics examination.

$\rightarrow\:\sf{\dfrac{75}{100}\:\times\:x}$

$\rightarrow\:\sf{\dfrac{3x}{4}}$ ...(3)

Also, 40 students fail in both english and mathematics.

$\therefore$ Number of students who passed in english only = Students passed in English - Students passed in both subjects.

$\implies\:\sf{\dfrac{4x}{5}\:-\:\dfrac{3x}{4}}$

$\implies\:\sf{\dfrac{16x\:-\:15x}{20}}$

$\implies\:\sf{\dfrac{x}{20}}$

Similarly,

Number of students who passed in mathematics only = Students passed in mathematics - Students passed in both subjects.

$\implies\:\sf{\dfrac{17x}{20}\:-\:\dfrac{3x}{4}}$

$\implies\:\sf{\dfrac{17x\:-\:15x}{20}}$

$\implies\:\sf{\dfrac{2x}{20}}$

$\implies\:\sf{\dfrac{x}{10}}$

Total number of students passed in examination = Students passed in english + Students passed in mathematics + Students passed in both subjects (maths and english)

$\implies\:\sf{\dfrac{x}{20}\:+\:\dfrac{x}{10}\:+\:\dfrac{3x}{4}}$

$\implies\:\sf{\dfrac{x\:+\:2x\:+\:15x}{20}}$

$\implies\:\sf{\dfrac{18x}{20}}$

$\implies\:\sf{\dfrac{9x}{10}}$

Now,

Number of students failed = Total number of students - Total number of students who passed in examination

$\implies\:\sf{x\:-\:\dfrac{9x}{10}}$

$\implies\:\sf{\dfrac{10x\:-\:9x}{10}}$

$\implies\:\sf{\dfrac{x}{10}}$

According to question,

$\implies\:\sf{\dfrac{x}{10}\:=\:40}$

$\implies\:\sf{x\:=\:40(10)}$

$\implies\:\sf{x\:=\:400}$

•°• Total number of students = 400

Answer 2

Question :------ we have to Find number of students.....

Given :------------

• 80% passed in english
• 85% passed in maths
• 75% passed in both maths and english
• 40 students failed in both subject ..

My solution :----------

Let Passed in maths = P(m) = 80%

Let passed in English = P(e) = 85%

Let no. of students pass in either math or english =

P( m ∪ e )

Let no.of students pass in both math and english =

P( m ∩ e ) = 75%

we know that :--------

P(A ∪ B) = P(A) + P(B) - P(A∩B)

Putting Values here we get,

P( m ∪ e ) = 80% +85% - 75%

P( m ∪ e ) = 90%

So,

no. of students pass in either math or english = 90%

Therefore Number of Students Failed in both either math or english are = 100-90 = 10% .....

it is given that , failed students are 40..

so,

10% ------------------- 40

10×10 ----------------- 40×10

100% ------------------ 400

so, Total students in class were 400 students ..