Question

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

• A. 34%
• B. 36%
• C. 64%
• D. 70%

Answer 1

The correct option is A 34%

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

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

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

$100=70+64-n(O\cap A)$
$n(O\cap A)=34\%$