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A survey was conducted among 200 users of mobile phones of differentcompanies. It was found that 160 use mobile phones of OnePlus, 100 usemobile phones of Samsung and 90 use mobile phones of LG. 20 use mobilephones of all three companies and each one uses mobile phones at least oneof the three companies. How many use mobile phones of only one company?​

Answer»

Given :   A survey was conducted among 200 users of mobile phones of DIFFERENT companies. It was found that 160 use mobile phones of OnePlus, 100 use mobile phones of Samsung and 90 use mobile phones of LG. 20 use mobile phones of all three companies and each one uses mobile phones at least one of the three companies.

To Find : How MANY use mobile phones of only one company

Solution:

refer the Venn diagram :

(140 - a -b)  +(80 - b - c)  + (70 - a  - c) + a + b + c + 20= 200

=>  (a + b + c)  = 110

=> a + b + c  = 110

use mobile phones of only one company

= (140 - a -b)  +(80 - b - c)  + (70 - a  - c)

= 290 - 2(a + b + c)

= 290 - 2(110)

= 70

70 use mobile phones of only one company

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