on set theory

Question

Every resident of a city can speak Hindi or English. If 75 % of the population speaks Hindi and 60% speaks English, then what percentage can speak both the languages ?

Answer 1

Let H = the set of people who speak Hindi and E = the set of people who speak English.

• n(H∪E) = all residents of the city = 100%
• n(H) = percent who speak Hindi = 75%
• n(E) = percent who speak English = 60%
• n(A∩E) = percent who speak both

 

n(H∪E) = n(H) + n(E) - n(A∩E)

 

Plug in the numbers and solve for n(A∩E).