A survey shows that 73 % of the persons working in an office like coffee, whereas 65 % like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be:

Question

A survey shows that 73 % of the persons working in an office like coffee, whereas 65 % like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be:, 63, 36, 54, 38

MARKS App · Accepted Answer

n C = 73 , n T = 65 , n C ∩ T = x , Considering that value of n C ∪ T cannot exceed 100 in terms of percentage, we get n C ∪ T ≤ 100 ⇒ n C + n T - n C ∩ T ≤ 100 ⇒ x ≥ 38 Therefore, x ≠ 36 . n C ∩ T ≤ min n C , n T ⇒ x ≤ 65 ⇒ 38 ≤ x ≤ 65 Hence x may assume values 63 , 54 , 38 .

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