7:37 pm

## Percent Problem: What Is The Total Number Of Students?

The percent problem is: In an examination, 60% of the candidates passed in English, 70% passed in mathematics, and 10% failed in both subjects. If 144 candidates passed in both, what is the total number of students?

## Steps to Get The Total Number Of Students

To solve this problem; the first approach is to set up the right equation. We will call it the main equation in which we will plug in all the variables to get the end result; the total number of students.

### Assuming Variables

Firstly, assume the total number of students is “x”

Secondly, assume the percentage of students who passed in English and mathematics “A”.

Thirdly, assume the percentage of students who passed in English and failed in mathematics “B”.

Fourthly, assume the percentage of students who failed in English and passed in mathematics “C”.

Finally, assume the percentage of students who failed in English and mathematics “D”.

### Setting Up Equations

Our goal is to get the percentage of students who passed in English and mathematics “A”. Then, we will solve the easy equation (Ax = 144) as it is given in the problem that 144 candidates passed in English and mathematics.

A + B + C + D = 100% → (1)

As given in the problem, the percentage of students who failed English and mathematics “D” is 10%. As a result:

A + B + C + 10% = 100% → (2)

Also, it is given in the problem that 60% of the candidates passed in English. In other words, 60% passed in English and mathematics “A” or  passed in English and failed in mathematics “B”. As a result:

60% = A + B or

B = 60% – A → (3)

Moreover, it is given in the problem that 70% of the candidates passed in mathematics. In other words, 70% passed in English and mathematics “A” or  failed in English and passed in mathematics “C”. As a result:

70%= A + C or

C = 70% – A →  (4)

Now, plug equations (3) and (4) in equation (2). As a result:

A + 60% – A + 70% – A + 10% = 100%

A – 2A + 130% = 90%

40% = A 0r A = 0.4

But we know that Ax = 144

Hence, 0.4x = 144

x = 360

Therefore, the total number of students is 360.