In survey among 195 people, it was found that 25 liked tea only and 125 coffee only.the number of people who liked coffee is 3 times the number of people who liked tea. By using Venn-diagram, find the number of people who liked both and who liked none of them?
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Given :
In a survey of 195 people
25 like only tea
125 love only coffee
Number of people like coffee is 3 times the number who liked tea.
To Find:
The number of people who like both and who like none of them.
In the figure i have attached below,
a represents the people who love tea only
c represents people who love coffee only
b represents people who love both tea and coffee.
d represents the total people undertaken survey
e represents people who don't like coffee and tea both.
a = 25 c = 125
a+b = people who like tea
b+c = people who like coffee.
3(a+b) = b+c (given)
3a + 3b = b+c
substitute values of a and c
3(25) + 2b = 125.
2b = 50.
b = 25
number of people who like both = 25
a + b + c + e = d = 195.
substitute values of a , b and c.
e = 195-25-25-125
e = 20
Number of people who like both = 25
Number of people who liked none of them = 20
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