Question
Each student in a class of 40, studies at least one of the subjects English, Mathematics and Economics. 16 study English 22 Economics and 26 Mathematics, 5 study English and Economics, 14 Mathematics and Economics, and 2 study all the three subjects. The number of students who study English and Mathematics but not Economics is :
A.
7
B.
5
C.
10
D.
4
Answer :
5
Solution :
$$C$$ stands for set of students talking Economics.
$$\eqalign{ & a + b + c + d + e + f + g = 40;\,\,\,a + b + d + g = 16 \cr & b + c + e + g = 22;\,\,d + e + f + g = 26 \cr & b + g = 5;\,\,e + g = 14;\,\,g = 2 \cr & {\text{Go by backward substitution}} \cr & e = 12,\,b = 3,\,d + f = 12,\,c + e = 17\,\, \Rightarrow c = 5;\,\,a + d = 11 \cr & a + d + f = 18\,\, \Rightarrow \,f = 7 \cr & \therefore \,\,d = 12 - 7 = 5 \cr} $$
$$C$$ stands for set of students talking Economics.
$$\eqalign{ & a + b + c + d + e + f + g = 40;\,\,\,a + b + d + g = 16 \cr & b + c + e + g = 22;\,\,d + e + f + g = 26 \cr & b + g = 5;\,\,e + g = 14;\,\,g = 2 \cr & {\text{Go by backward substitution}} \cr & e = 12,\,b = 3,\,d + f = 12,\,c + e = 17\,\, \Rightarrow c = 5;\,\,a + d = 11 \cr & a + d + f = 18\,\, \Rightarrow \,f = 7 \cr & \therefore \,\,d = 12 - 7 = 5 \cr} $$