Question

In class of 130 students, 85 passed in mathematics, 60 passed in social studies and 10 failed in both the subjects. How many students passed in both subjects

Answer 1

The number of students passed in both subjects is 25.

In a class of 130 students, 85 passed in mathematics, 60 passed in social studies and 10 failed in both the subjects.

We have to find the number of students passed in both subjects.

Here, 10 students failed in both the subjects, it means, (130 - 10) = 120 students passed in at least one subject.

Now, number of students passed in mathematics = 85

number of students passed in social studies = 60

∴ total number of students passed in either mathematics or social studies = 85 + 60 = 145

∵ 120 students passed at least one subject.

∴ total number of students passed in both subjects = 145 - 120 = 25

Therefore the number of students passed in both subjects is 25.

Short method : n(U) = 130 , n(A ∩ B)' = 10 , n(A) = 85 and n(B) = 60

n(A ∪ B) = n(U) - n(A ∩ B)' = 130 - 10 = 120

Now, n(A ∩ B) = n(A) + n(B) - n(A U B)

= 85 + 60 - 120 = 25

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Answer 2

Total number of students in a class = 130                              ( given)

total number of students passed in mathematics = 85       (given)

total number of students passed in social studies=60         ( given)

total number of students failed in both the subjects=10       (given)

According the question we have to find the number of students passed in both subjects.

According sum, 10 students failed in both the subjects,

that means, (130 - 10) = 120 students passed in at least one subject. number of students passed in mathematics = 85

number of students passed in social studies = 60

Hence total number of students passed in either mathematics or social studies = (85 + 60) = 145

It is known that 120 students passed at least one subject.

Therefore total number of students passed in both subjects = (145 - 120) = 25

Ans:- Total number of students passed in both subjects will be 25.

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