Question

in a class of 55 students 15 students like math but not english and 18 students like english but not math if 5 students do not like both subjects how many students like both subjects

Answer 1

Answer:

17

Step-by-step explanation:

total students = 55

5 students do not like both subjects = 55-5 = 50

15 students like math but not english= 50-15 = 35

18 students like english but not math = 35-18 = 17

17 students like both subjects

Answer 2

$\large\underline{\bf{Solution-}}$

Given that :-

• Total number of students in class = 55

• Number of students like Math but not English = 15

• Number of students like English but not Maths = 18

• Number of students who didn't study English and Maths = 5

Now,

Let assume that

• A be the set of students like Maths

• B be the set of students like English

According to statement,

$\rm :\longmapsto\:n(A \: \cup \: B) = 50$

$\rm :\longmapsto\:n(A - B) = 15$

$\rm :\longmapsto\:n(B - A) = 18$

We know that,

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

$\rm :\longmapsto\:50 = 15 + 18 + n(A\cap B)$

$\rm :\longmapsto\:50 = 33 + n(A\cap B)$

$\rm :\longmapsto\:50 - 33 = n(A\cap B)$

$\bf\implies \:n(A\cap \: B) = 17$

Hence,

• Number of students like both subjects = 17

Additional Information :-

$\green{\boxed{ \tt \: n(A - B) = n(A) - n(A\cap \: B)}}$

$\green{\boxed{ \tt \: n(B - A) = n(B) - n(A\cap \: B)}}$

$\green{\boxed{ \tt \: n(A\cup \: B) = n(A) + n(B) - n(A\cap \: B)}}$