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Study information given and select valid conclusion/s from the given statements based on it. In a joint family the number of members who take only coffee is equal to the half the number of members who take tea and the number of persons who take only tea is equal to the half the number of persons who take coffee. Statements: a. The total number of persons who take either coffee or tea or both is thrice the number of persons who take only coffee or only tea. b. The total number of persons who take only coffee and those who take only tea is twice the number of persons who take both coffee and tea.

Study information given and select valid conclusion/s from the given statements based on it. In a joint family the number of members who take only coffee is equal to the half the number of members who take tea and the number of persons who take only tea is equal to the half the number of persons who take coffee. Statements: a. The total number of persons who take either coffee or tea or both is thrice the number of persons who take only coffee or only tea. b. The total number of persons who take only coffee and those who take only tea is twice the number of persons who take both coffee and tea. Correct Answer Both a and b

Let us assume

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If the number of persons who take only coffee (c) = x;

 the number of members who take tea (a + b) = 2x.

the number of persons who take coffee(a + c) = 2 the number of persons who take only tea is equal to the half(c) = 2x

This implies that (a + b) = (a + c) = 2x; b = c = x = a; 

Now analyzing the statements:

a. The total number of persons who take either coffee or tea (a + c) or both (b) is thrice the number of persons who take only coffee or only tea. 

This implies that

a + b + c = 3 c or a + b + c = 3a 

Since, a = b = c both the above conditions hold true.

b. The total number of persons who take only coffee(c)  and those who take only tea(a) is twice the number of persons who take both coffee and tea(b)

This implies that a + c =2b

Since, a = b = c  the above condition hold true.

Hence, both the statements a and b are valid.

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