Question

If $63$ % of persons like oranges while $76$ % like apples, what can be said about % of persons who like both oranges and apples? Each person eats at least one fruit

• A. $39$%
• B. $41$%
• C. $43$%
• D. $45$%

Answer 1

The correct option is A $39$%

From the given data

$n\left(O\right)=0.63$

$n\left(A\right)=0.76$

$n(A\cup O)=1$ as every person eats at least one fruit

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

$1=0.63+0.76-n(A\cap B)$

$n(A\cap B)=1.39-1$

$n(A\cap B)=0.39$

$A\cap B=0.39\times 100=39$

Hence $39$% of people eat both orange and apple