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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

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