In a group 40% people like only milk, 20% like only tea and 20% like only coffee, if 2% like all the three drinks and 8% like both milk and coffee, 7% like both coffee and tea and 9% like both tea and milk, then how many percent of people like only two drinks?

In a group 40% people like only milk, 20% like only tea and 20% like only coffee, if 2% like all the three drinks and 8% like both milk and coffee, 7% like both coffee and tea and 9% like both tea and milk, then how many percent of people like only two drinks? Correct Answer 18%

Given :

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Number of people who only like milk n(M) = 40%

Number of people who only like Tea n(T) = 20%

Number of people who only like coffee n(C) = 20%

Number of people who like all the three drinks n(M ⋂ T ⋂ C) = 2%

Number of people who like milk and coffee n(M ⋂ C) = 8%

Number of people who like coffee and tea n(C ⋂ T) = 7%

Number of people who like milk and tea n(M ⋂ T) = 9%

∴ Number of persons who like milk and coffee only = n(M ⋂ C) – n(M ⋂ T ⋂ C) = 8% – 2% = 6%

Number of persons who like coffee and tea only = n(C ⋂ T) – n(M ⋂ T ⋂ C) = 7% – 2% = 5%

Number of persons who like milk and tea only = n(M ⋂ T)  – n(M ⋂ T ⋂ C) = 9% – 2% = 7%

∴ Number of persons who like only two drinks = 6% + 5% + 7% = 18%

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