Question

In a survey of 800 students in a school 200 were listed as taking apple juice, 250 taking orange juice and 125 were taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.

Answer 1

the student who taking either orange or apple =( 200+250)-125=325
so the student who taking neither apple nor orange juice=800-325=475

Answer 2

The Number of students who were taking neither apple juice nor orange juice is 475.

Step-by-step explanation:

We are given that in a survey of 800 students in a school 200 were listed as taking apple juice, 250 taking orange juice and 125 were taking both apples as well as orange juice.

Let the total number of students in school = n(T) = 800

Number of students who were taking apple juice = n(A) = 200

Number of students who were taking orange juice = n(O) = 250

Number of students who were taking both apples as well as orange juice = n(A $\bigcap$ O) = 125

Now, the number of students who takes either apple juice or orange juice is given by = n(A $\bigcup$ O)

 

So, n(A $\bigcup$ O)  =  n(A) + n(O) - n(A $\bigcap$ O)

                      =  200 + 250 - 125

     n(A $\bigcup$ O)  =  325

So, there are 325 students who take either apple juice or orange juice.

Now, the number of students taking neither apple juice nor orange juice = n(T) - n((A $\bigcup$ O) = 800 - 325 = 475.