In an examination, 56% of the candidates failed in English and 48% failed in science. If 18% failed in both English and science, find the percentage of those who passed in both the subjects.

Question

Philoid · Accepted 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%