Question

In a survey of some students, it was found that 60 % of the students were studying commerce and 40 % were studying science. If 40 students were studying both the subjects and 10% did not study any of two subjects, by drawing a Venn-diagram,
(i) find the total number of students.
(u) Find the number of students who were studying science only.​

Answer 1

Answer:

Let total be U where who were studying Commerce be 'C' and Science be 'S'.

n(C)= 60%

n(S)= 40%

n(C'U'S)= 10%

n(C∩S)= x

now,

U= no(C)+no(S)+n(C∩S)+n(C'U'S)

100=60-x+40-x+x+10

100=110-x

100-110=-x

-10=-x

hence, x=10 %

then, according to the question,

10% of U= 40

10/100*U=40

U=40000/10

therefore, U= 4000

again,

no(S)= n(S)- n(C∩S)

       = 40% of U - 40

       =40/100*4000-40

       =1600-40

       =1560