Question

In a combined test in math and chemistry; $84\% $ candidates passed in math; $76\% $ in chemistry and $8\% $ failed in both. Find the percentage of failed candidates.

Answer 1

Hint: Here in this question know the percentage of students passed in math and the percentage of students passed in chemistry. So, from that we can get the value of the percentage of students who failed in math and percentage of students who failed in chemistry.
After that by subtracting the percentage of students who failed in both subjects from their sum we will get the answer.
That is
Percentage of students failed$ = $(percentage of students failed in math)$ + $(percentage of students failed in chemistry)$ - $( percentage of students failed in both subjects)

Complete Step by Step solution:
First of all we will start solving after enlisting the given information in the question.
So, it is given that
There were two tests taken one of math and other of chemistry
$84\% $ candidate passed in math
$76\% $ candidates passed in chemistry
$8\% $ candidates failed in both.
So, from the given information we can say that
Percentage of students failed in the math test$ = $total percentage(i.e $100\% $)$ - $(percentage of students passed in math test)
$ \Rightarrow $ Percentage of students failed in the math test$ = 100\% - 84\% $
$ \Rightarrow $ Percentage of students failed in the math test$ = 16\% $ ……………..(i)
And also,
Percentage of students failed in the chemistry test$ = $total percentage (i.e $100\% $)$ - $(percentage of students passed in chemistry test)
$ \Rightarrow $ Percentage of students failed in the chemistry test$ = 100\% - 76\% $
$ \Rightarrow $ Percentage of students failed in the chemistry test$ = 24\% $ ……………..(ii)
And also it is given that $8\% $ candidates failed in both.
So, as we know that
Percentage of students failed$ = $(percentage of students failed in math)$ + $ (percentage of students failed in chemistry) $ - $( percentage of students failed in both subjects)
$ \Rightarrow $ By putting the corresponding values we will get our answer. So,
Percentage of students failed $ = 16\% + 24\% - 8\% $
$ \Rightarrow $ Percentage of students failed $ = 32\% $
$\therefore 32\% $ of total students failed.

Note: In this question, we can also solve it by firstly creating a Venn diagram of the given information which will help you to remember each and every given value whenever you need while solving the question and will also give you the clear view of what quantities we have to find to solve the question.