Q. 94.0( 4 Votes )

In an examination

Answer :

Given:


In an examination:


- 56% of candidates failed in English


- 48% of candidates failed in science


- 18% of candidates failed in both English and Science


To Find;


Percentage of students who passed in both subjects.


Let us consider,


Percentage of candidates who failed in English = n(E) = 56


Percentage of candidates who failed in Science = n(S) = 48


Percentage of candidates who failed in English and Science both


= n(E S) = 18


Percentage of candidates who failed in English only = n(E - S)


Percentage of candidates who failed in Science only = n(S - E)


Venn diagram:



Now,


n(E - S) = n(E) - n(E S)


= 56 – 18


= 38


n(S - E) = n(S) - n(E S)


= 48 – 18


= 30


Therefore,


Percentage of total candidates who failed =


n(E - S) + n(S - E) + n(E S)


= 38 + 30 + 18 = 86%


Now,


The percentage of candidates who passed in both English and


Science = 100 - 86 = 14%


Hence,


The percentage of candidates who passed in both English and


Science = 14%


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