SETS B9

In a certain school, 200 students take either Commerce or biology. 150 take commerce and 120 take both subjects. Find those who take biology only.

Solution

In most cases, OR stands for union whereas AND/BOTH, stands for intersection.

Let Biology = n(B), commerces = n(C).

n(C)= 150 ,

n(B)= ?

n(BuC) = 200,

n(BnC)= 120

Solution

n(CuB) = n(C) + n(B) - n(CnB)

200  =  150 + n(B) – 120

200  =  n(B) + 30

200 - 30  =  n(B)

n(B)= 170

Biology only = n(B) – n(CnB)

                         = 170 – 120

                         = 50 

Hence those taking only biology are 50.      

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TRY THIS……………………

In a certain school, 300 students take either Commerce or biology. 150 take commerce and 100 take both subjects. Find those who take biology only.