Question

In a class of $25$ students, $12$ have taken Mathematics, $8$ have taken Mathematics but not Biology. If each student has taken atleast one subject, find the number of students who have taken
i) Biology but not Mathematics
ii) Both mathematics and biology

Answer 1

class = 25

$T=M+B+B^{\prime }$

where M = students taken

maths only

B = students taken Biology only

$B^{\prime }$ = students taken both.

8 = maths only (M)

$12=M+B^{\prime }$

$\therefore M+B^{\prime }-M=B^{\prime }=12-8=4$

$\therefore B^{\prime }=4$ students

and $25=7=M+B+B^{\prime }=B+4+B$

$B=13$

i) Biology but not maths $\Rightarrow 13$ (B)

ii)Both $\Rightarrow \left(B^{\prime }\right)\Rightarrow 4$