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Home » In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows: French = 17, English = 13, Sanskrit = 15 French and English = 09, English and Sanskrit = 4 French and Sanskrit = 5, English, French and Sanskrit = 3. Find the number of students who study (i) French only (ii) English only
In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows: French = 17, English = 13, Sanskrit = 15 French and English = 09, English and Sanskrit = 4 French and Sanskrit = 5, English, French and Sanskrit = 3. Find the number of students who study (i) French only (ii) English only
CBSE | Class 11 | Maths | NCERT Exemplar | Sets
In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows: French = 17, English = 13, Sanskrit = 15 French and English = 09, English and Sanskrit = 4 French and Sanskrit = 5, English, French and Sanskrit = 3. Find the number of students who study (i) French only (ii) English only

Solution:

Given,

50 = Total number of students

13 = Number of students studying English

17 = Number of students studying French

15 = Number of students studying Sanskrit

9 = Number of students studying English and French

5 = Number of students studying French and Sanskrit

4 = Number of students studying English and Sanskrit

3 = Number of students studying all three subjects

Let U be the total number of students

Let E be the number of students studying English

Let F be the number of students studying French

Let S be the number of students studying Sanskrit

NCERT Exemplar Class 11 Maths Chapter 1-14

\Rightarrow 3+c=4

\Rightarrow c=1

n(F)=e+d+a+b=17 \Rightarrow e+2+3+6=17

\Rightarrow e+11=17

\Rightarrow e=6

\Rightarrow f(E)=g+c+a+b=13

\Rightarrow g+1+3+6=13

\Rightarrow g+10=13

\Rightarrow g=3

n(S)=f+c+a+d=15

\Rightarrow f+1+3+2=15

\Rightarrow f+6=15

\Rightarrow f=9

As a result, from the above equations, we have,

(i) e = 6 = No. of students studying French only

(ii) g = 3 = No. of students studying English only

i

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