Question

In Bank PO Prelims Examination, 30% of the candidate failed in English, 45% failed in Quantitative aptitude, and 10% failed in both subject. Find the percentage of those candidates who passed in both subject. 
1. 35%
2. 45% 
3. 65% 
4. 25% 
5. 55%

Answer 1

Correct Answer - Option 1 : 35%

Given 

Percentage of candidate who failed in English = 30% 

Percentage of candidate who failed in Quantitative = 45% 

Formula Used 

Percentage = (Actual/Total) × 100 

Calculation 

Let the number of students be 100.

Number of students who failed in English is 30%

⇒ n(H) = 30

Number of students who failed in Quantitative is 45% 

⇒ n(E) = 45

Number of students who failed in both the subjects is 10%

⇒ n(H ∩ E) = 10

Applying the set theory rule,

⇒ n (H U E) = n(H) + n(E) – n(H ∩ E) 

⇒ 30 + 45 – 10 = 65

⇒ Percentage of students who failed in English or Quantitative or both the subjects = 65%

⇒ Number of students who passed in both the subjects = 100 – 65 = 35%

∴ Number of students who passed in both the subjects  is 35%