37 Maths -- Set

Q. Out of 200 people in a village, 150 can speak Newari language, 80 can speak Bhojpuri, while 30 can't speak any languages. By drawing venn diagram, find the number of people speaking different languages.                                                            • Who can speak both o...

Q. Out of 200 people in a village, 150 can speak Newari language, 80 can speak Bhojpuri, while 30 can't speak any languages. By drawing venn diagram, find the number of people speaking different languages.                                                            • Who can speak both of the languages?      • Who can speak at least one language?        • Who can speak only one language?

Let N and B denote the set of people whi can speak Newari and Bhojpuri reapectively.

Now, n(U)=200, n(N)=150, n(B)=80 and (A∩ B)' = 30 

i) Let (A∩ B) = x

Representing above information in a venn diagram.

From the venn diagram,

150-x + x +80-x + 30=200

Or,  260-x = 200

Or, x= 260-200

Therefore, x=60.

ii) n(N∪B) = n(N)+ n(B) - n(N∩B)

                   = 150 + 80 - 60

                   = 170

iii) n०(N)+ n०(B)= 150-x + 80-x

                             = 150-60+80-60

                             = 110

Therefore,

No.of people speaking both language=60

No.of people speaking at least one language= 170

No.of people speaking only one language= 110

More questions on Set

Close Open App