Question

2. In a group of 50 persons , 15 drink tea, but not coffee and 21 drink tea. How many
drink coffee but not tea, if every person in the group takes atleast one beverage​

Answer 1

14 are drink coffee

Step-by-step explanation:

how many persons in a group = 50

how many persons drink Tea = 15

+ 21

______

36

now 50 - 36 = 14

14 persons are drink coffee

Answer 2

☆ Given Question:-

In a group of 50 persons , 15 drink tea, but not coffee and 21 drink tea. How many drink coffee but not tea, if every person in the group takes atleast one beverage.

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$\huge{AηsωeR }$

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☆ Let A denotes the set of persons who drink tea and Let B denotes the set of persons who drink Coffee.

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Given that :-

• Total persons = 50 persons
• 15 drink tea, but not coffee
• 21 drink tea

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$\begin{gathered}\bf\red{According \: to \: statement}\end{gathered}$

$\sf \:  ⟼ \: n(A∪B) \: = \: 50$

$\sf \:  ⟼n(A−B) \: = 15$

$\sf \:  ⟼n(A) \: = \: \: 21$

$\bf\implies \:n(A−B) + n(A∩B) = 21$

$\sf \:  ⟼15 + n(A∩B) = 21$

$\sf \:  ⟼n(A∩B) = 6$

☆Now, Using formula

$\sf \:  ⟼n(A∪B) = n(A) \: + \: n(B) \: - n(A∩B)$

☆ On substituting the values from above, we get

$\bf\implies \:50 = 21 + n(B) - 6$

$\sf \:  ⟼50 = 15 + n(B)$

$\sf \:  ⟼n(B) = 35$

Now, the number of persons who drink coffee but not tea is given by

$\bf\implies \:n(B - A)  = n(B) - n(A∩B)$

$\bf\implies \:n(B - A)  = 35 - 6 = 29$

⇒ The number of persons who drink coffee but not tea is 29.

=14 

⇒n(A)−=14 

n(A)−14=30−14=16.