Question

in an examination 70% examinees passed in business mathematics and 65% in financial accounting while 15% failed in both the subjects .it 2700 examiees passed in both subjects find the total number ofexamiees

Answer 1

Answer: Suppose for business mathematics B and financial accounting F then

n(U) =100 %

n(B) =70 %

n(F)= 65%

n(B intersection F ) = ?

n(B union F whole bar )=15 %

n(B intersection F ) = 2700

Now

n(U) =n(B) +n(F) -n(B intersection F) + n(B Union F whole bar F)

100=70+65-n(B intersection F)+15

100=150-n(B intersection F)

n(B intersection F)=50 %

now,

n(B intersection F)=2700

Let n(U) =X

50 % percent of X =2700

50%*X =2700

50÷100X =2700

X= 2700*2

X =5400

Hence total no of examinee are 5400.

Answer 2

Given,

Percent of examinees who passed in business mathematics = 70 percent

Percent of examinees who passed in financial accounting = 65 percent

Percent of examinees who failed both = 15 percent.

Number of examinees who passed in both the subjects = 2700

To find,

The total number of examinees

Solution,

The total examinees are 5400.

We can solve this mathematical problem by the following process.

Let the number of students be x.

Number of examinee who passed business mathematics = $\frac{7x}{10}$

Number of examinee who passed financial accounting = $\frac{65x}{100}$

Number of examinee who failed both = $\frac{15x}{100}$

Number of student who passed = $\frac{85x}{100}$

Thus,

The number of students who passed both the subjects = $\frac{70x}{100}+\frac{65x}{100} - \frac{85x}{100}$

                                                                                             = $\frac{50x}{100}$

We know that,

The number of students who passed both = 2700 = $\frac{x}{2}$

The total number of students = x = 2700 x 2

                                                       = 5400.

As a result, the total number of students are 5400.