Question

In a village there are 60 families. Out of these 28 families speak only Tamil and 20
families speak only Urdu. How many families speak both Tamil and Urdu.

Answer 1

Let
n(A) denote no. of people speak tamil
n(B) denote no. of people speak urdu
no. of families speak only tamil=n(A/B)=n(A)-n(A n B)=28
no. of families speak only urdu=n(B/A)=n(B)-n(A n B)=20
Total no. of families=n(U)=60
each family can speak either tamil and urdu
(assume that they don't speak any other language than tamil or urdu)
so
n(U)=n(A U B)=n(A)+n(B)-n(A n B)=60...(1)
asn(A/B)+n(B/A)=n(A)-n(A n B)+n(B)-n(A n B)=n(A)+n(B)-2n(A n B)=48..(2)
(1)-(2)
 {n(A)+n(B)-n(A n B)}-{n(A)+n(B)-2n(A n B)}=n(A n B)=60-48=12

Answer 2

total families =60
families who only speak tamil=28
families who only speak urdu=20
total families speaking only  tamil and urdu =28+20=48
now the families who speak both tamil and urdu=60-48=12
 so the families who speak both urdu and tamil=12