In an examination 42% students failed in Mathematics and 52% failed in Science. If 17% failed in both the subjects, find the Percentage of those Who Passed in both the subjects.

Given:-

42% students failed in Mathematics

52% students failed in Science

17% students failed in both the subjects

Formula Used:

⇒ n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

Here,

n(A ∪ B) = union of two sets A and B 

n(A) = Number of elements in A

n(B) = Number of elements in B

n(A ∩ B) = The number of elements that are common to both A and B

Calculation:

Let total 100 students there in the examination

Thus, students who failed in Hindi n(H) = 42

Students who failed in English n(E) = 52

Total students who failed in both n(H ∩ E) = 17

Now, the number of students who passed both subjects,

⇒ n(H ∪ E) = n(H) + n(E) − n(H ∩ E)

⇒ n(H ∪ E) = 42 + 52 − 17

⇒ n(H ∪ E) = 77

In percentage,

\(⇒ p\%= \dfrac{100-77}{100}\times100\)

⇒ p% = 23%

So, the percentage of those students who passed both subjects is 23%.

Hence, the correct option is 1.

Alternate Method 
Percentage of students failed only in Science = (52 – 17)% = 35%

Percentage of students failed only in Mathematics = (42 – 17)% = 25%

Percentage of students Failed = (35 + 25 + 17)% = 77%

Percentage of students passed in both subjects = (100 – 77)%

⇒ 23%

∴ The percentage of students who passed in both subjects is 23%