In an examination of a certain class, at least 70% of the students failed in Physics, at least 72% failed in Chemistry, at least 80% failed in Mathematics and at least 85% failed in English. How many at lest must have failed in all the four subjects ?
To find the minimum number of students who failed in all four subjects, we need to find the highest percentage of students who failed in each subject.
Given that at least 70% failed in Physics, at least 72% failed in Chemistry, at least 80% failed in Mathematics, and at least 85% failed in English, we take the maximum percentage from each subject.
So, the maximum percentage of students who failed in all four subjects is 85%.
Therefore, at least 85% of the students must have failed in all four subjects.
To find the minimum number of students who failed in all four subjects, we need to determine the highest percentage of students who failed in any individual subject.
Let's start by finding the highest failure percentage among the four subjects given:
Physics: At least 70% failed.
Chemistry: At least 72% failed.
Mathematics: At least 80% failed.
English: At least 85% failed.
In order to find the highest percentage of students who failed in any subject, we need to find the subject with the highest failure rate.
In this case, the subject with the highest failure rate is English, with at least 85% failing.
Therefore, we can conclude that at least 85% of the students failed in all four subjects.
So, the minimum number of students who failed in all four subjects is 85%.
Let's start with Physics and Chemistry.
at most 30% passed physics
at most 28% passed chemistry
so, at most 58% passed either of the two subjects.
That is, the % who failed both is at least 42%
That is 100-(30+28)%
Now extend that to the other subjects.