Question

In an examination 80% candidates passed in english and 85% candidates passed in mathematics. if 73% candidates passed in both these subjects, then what per cent of candidates failed in both the subjects?

Answer 1

Students passed in English = 80%
Students passed in Math's = 85%
Students passed in both subjects = 73%
Then, number of students passed in at least one subject = (80+85)-73 = 92%.
[The percentage of students passed in English and Maths individually, have already included the percentage of students passed in both subjects. So, We are subtracting percentage of students who have passed in both subjects to find out percentage of students at least passed in one subject.]
Thus, students failed in both subjects = 100-92 = 8%.

Answer 2

Given :

In an examination

%age of candidates passed in English subject = 80%

%age of candidates passed in Mathematics subject = 85%

%age of candidates passed in both subject = 73%

To Find :

%age of candidates failed in both subject

Solution :

Let The total number of candidates in examination = 1000

So, The number of candidates passed in English subject =  80% of 1000

                                                                                               = $\dfrac{80}{100}$ × 1000

                                                                                               = 800

Again

The number of candidates passed in Mathematics subject =  85% of 1000

                                                                                                  = $\dfrac{85}{100}$ × 1000

                                                                                                  = 850

Similarly

The number of candidates passed in both subject =  73% of 1000

                                                                                     = $\dfrac{73}{100}$ × 1000

                                                                                     = 730

Now,

Number of candidates failed in both subjects = Total candidates - [  ( number of candidates passed in English subject + number of candidates passed in Mathematics subject ) -  number of candidates passed in both subject ]

Or, Number of candidates failed in both subjects = 1000 - [ ( 800 + 850) - 730 ]

Or,                                                                              = 1000 - [ 1650 - 730 ]

or,                                                                               = 1000 - 920

∴ Number of candidates failed in both subjects = 80

Now,

%age of candidates failed in both subjects = $\dfrac{Number of candidates failed in both subjects }{Total number of candidates}$ × 100

i.e                                    = $\dfrac{80}{1000}$ × 100 = 8%

Hence, The %age of candidates failed in both subjects is 8%  Answer