Question

In a class containing 120 students, 65 students drink tea and 84 students drink coffee. It x students drink both tea and coffee, what is the value of x ?

• A. 39
• B. 65
• C. $29\le x\le 65$
• D. $29\le x\le 84$

Answer 1

Answer: (C)

Let T denote the set of students who drink Tea and C denote the set of students who drink coffee. As given:
n (T) = 65, n (C) = 84,
Let x denote number of students who take tea and coffee both.
n(T $\cup$ C) = 120 and n(T $\cap$ C) = x
n(T $\cup$ C) = n(T) + n(C) - n(T $\cap$ C)
$\Rightarrow 120\ge 65+84-x$
$x\ge 149-120\ge 29$ and $x\le n(T)$
$\Rightarrow x\le 65\therefore 29\le x\le 65$