Question

In an examination out of 400 students, 75% passed in physics and 65% passed in mathematics. If 18% failed in both subjects, how many students passed in both subjects?
1. 232
2. 204
3. 168
4. 196

Answer 1

Correct Answer - Option 1 : 232

Given:

Per cent of passed students in Mathematics = 65% 

Per cent of passed students in Physics = 75% 

Failed in both the subjects = 18% 

The total number of students is 400

Concept used:

(A ∪ B) = (A) + (B) – (A ∩ B)

(A ∪ B) → Total

(A) → Part of A

(B) → Part of B

(A ∩ B) → The common part of A and B 

Calculations:

The number of students passed in at least one subject = 100 - 18 = 82%

Students passed in at least one subject (A ∪ B) = 82%

Students passed in Mathematics (A) = 65%

Students passed in Physics (B) = 75%

Students passed in both subjects = (A ∪ B)

82% = 65% + 75% - (A ∪ B)

⇒ (A ∪ B) = 140% - 82% = 58%

Now, 58% of 400 students

400 × (58/100) = 232

∴ The number of students passed in both subjects is 232.