Question

In Mohan's class, there are 30 students.
20 students are good at maths, 18 students
are good at history and 12 students are good
at both the subjects.
Draw a Venn diagram and using that find
the following:
Number of students good at maths only
b. Number of students good at history only
Number of students good at at least one
subject
d. Number of students good at neither of two​

Answer 1

Given :-

Students good in maths are 20

Students good in History are 12

Total number of students are 30

To Find :-

Students good at maths only

Students good at history only

Students good at neither subject.

Solution :-

$\sf{ Total \: = n(Maths) +n (History) - n(Maths \cap \: History) + students\ good\ in\ neither\ sub. }$

$\sf{30 \: = 20 +18 - 12 + x }$

$\sf{30 \: = 38 - 12 + x }$

$\sf{30 \: = 26 + x }$

$\sf{x = 4 }$ .

So 4 students are good at neither subject .

→ Students good at only Maths = Students good at maths - students good at both subjects

→ 20 - 12

→ 8 students are good at only maths .

→ Students good at only history = Students good at history - students good at both subject.

→ 18 - 12

→ 6 students are good at only history .