7. In a survey among a group of employees of a central Govt. office in Assam, it was found that 80 of them can speak the Assamese, 70 of them can speak English and 50 of them can speak both Assamese and English. If each of the employees who took part in the survey can speak either Assamese or English or both of the two languages, then find (i) the total number of employees who participated in the survey? (ii) how many of them can speak Assamese only? (iii) how many of them can speak English only? Advance Math Class 10 - Exercise: 1.1

In a survey among a group of employees of a central Govt. office in Assam, it was found that 80 of them can speak the Assamese, 70 of them can speak English and 50 of them can speak both Assamese and English. If each of the employees who took part in the survey can speak either Assamese or English or both of the two languages, then find (i) the total number of employees who participated in the survey? (ii) how many of them can speak Assamese only? (iii) how many of them can speak English only?

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Solution:

Let the set of employees can speak Assamese be A and the set of employees can speak English be E

Given, 

n(E)= 70,

n(AꓵE)= 50,

(i) We know that,

n(AUE)= n(A) + n(E) – n(AꓵE)

             = 80 + 70 – 50

             = 100

Therefore, the total number of employees= 100

(ii) the number of employees who can speak Assamese only 

= n(AUE) – n(E)

= 100 – 70

= 30

(iii) the number of employees who can speak English only 

= n(AUE) – n(A)

= 100 – 80

= 20

  Exercise: 1.1  

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