Question
A dinner party is to be fixed for group of 100 persons. in this party, 50 persons do not prefer fish, 60 prefer chicken and 10 do not prefer either chicken or fish. The number of persons who prefer both fish and chicken is :
A.
20
B.
22
C.
25
D.
none of these
Answer :
20
Solution :
Total number of persons $$ = a + b + c + n = 100$$
Do not prefer fish $$b + n = 50$$
$$60$$ prefer chicken hence $$b + c = 60$$
Do not like fish and chicken is $$n = 10$$
On solving these equations we will get $$a = 30,\,b = 40,\,c = 20$$
The number of persons who prefer both fish and chicken is $$ = c = 20$$
Total number of persons $$ = a + b + c + n = 100$$
Do not prefer fish $$b + n = 50$$
$$60$$ prefer chicken hence $$b + c = 60$$
Do not like fish and chicken is $$n = 10$$
On solving these equations we will get $$a = 30,\,b = 40,\,c = 20$$
The number of persons who prefer both fish and chicken is $$ = c = 20$$