Question

In a factory all the workers like oranges or apples. If $70\%$ of the workers like oranges and $64\%$ likes apples and $x\%$ like both oranges and apples, then x = ____.

• A. x ≥ 34
• B. x ≤ 64
• C. 34 ≤ x ≤ 64
• D. None of these

Answer 1

The correct option is A

x ≥ 34

Let U = 100

As all the workers like oranges or apples $n(O\cup A)$ = 100

n(O) = 70, n(A) = 64, $n(O\cap A)$ = x

We know, $n(O\cup A)$ = n(O) + n(A) - $n(O\cap A)$

$100=70+64-n(O\cup A)$

$n(O\cup A)$ = 34%