In a Board exam, 53% passed in Biology, 61% passed in English, 60% in Social Studies, 24% in Biology & English, 35% in English & Social Studies, 27% in Biology & Social Studies and 5% in none. Percentage of passes in all the three subjects is _____

Given:

Biology passed: 53%

English passed: 61%

Social Studies passed: 60%

Biology & English passed: 24%

English & Social Studies passed: 35%

Biology & Social Studies passed: 27%

None passed: 5%

Calculation:

Total passed: 100% - 5% = 95%

Let B = Biology, E = English, S = Social Studies

n(B) = 53, n(E) = 61, n(S) = 60

n(B ∩ E) = 24, n(E ∩ S) = 35, n(B ∩ S) = 27

Let n(B ∩ E ∩ S) = x

Using the formula:

n(B ∪ E ∪ S) = n(B) + n(E) + n(S) - n(B ∩ E) - n(E ∩ S) - n(B ∩ S) + n(B ∩ E ∩ S)

95 = 53 + 61 + 60 - 24 - 35 - 27 + x

95 = 174 - 86 + x

95 = 88 + x

x = 95 - 88

x = 7

∴ 7% passed in all three subjects.