A survey was conducted to find out the number of languages spoken by t

Number of employees = 210
Number of employees who did not speak English = 60
So, the number of employees who spoke English = 210 – 60 = 150

Number of employees who did not speak German = 150
So, number of employees who spoke German = 210 – 150 = 60

Number of employees who did not speak French = 170
So, number of employees who spoke French = 210 – 170 = 40

Number of employees who did not speak German or English = 20
So, these employees must speak only French (because it’s given that each employee speaks at least one language)

Number of employees who did not speak French and English = 20
So, these employees must speak only German (because it’s given that each employee speaks at least one language)

To Find: Maximum number of employees who spoke only English

To max the no. who only spoke English we need to reduce as little as possible from 150 (no. who spoke English)
We know French in total is 40, which means that max overlap between French/German/English can be 20. That leaves 20 of german out of the overlapping circles. This 20 needs to get subtracted from 150 of English. Hence max English will be 150-20=130

The explanation will help greatly if you try to understand it with a diagram.