In a certain state 60% are married employees and 52% graduate employees. 32% are neither married nor graduate employees. Find the percentage of married and graduate employees:

Given:

n(Married) = 60%

n(Graduate) = 52%

n(Neither married nor graduate) = 32%

Space = 100% - 32% = 68%

Concept used:

n(A ∪ B) = n(A) +n(B) - n(A ∩ B)

Calculation:

⇒ 68% = 60% + 52% - n(A ∩ B)

⇒ n(A ∩ B) = 112% - 68% = 44%

∴ The percentage of married and graduate employees is 44%.

Shortcut Trick 

Let the total employee be 100%

32% employees are neither graduates nor married.

So, employees either married or graduate = 100 - 32 = 68%

As per fig Married or graduate employee = 60 + 52 = 112%

So, The percentage of employee who are married and graduate = 112 - 68 = 44%

∴ The percentage of married and graduate employees is 44%.