Question

110 children choose their favourite colour from blue and pink. Every student has to choose at least one of the colour. 60 Children choose blue colour, while 70 children choose pink colour. How many children choose both the colours as their favourite colour?

Answer 1

Let A and B denote the respective children who chose blue and pink as their favourite colours.
Given: n(A) = 60, n( B) = 70, n$\left(\mathrm{A}\cup \mathrm{B}\right)$ = 110
We have to find n$\left(\mathrm{A}\cap \mathrm{B}\right)$.
Now, n$\left(\mathrm{A}\cup \mathrm{B}\right)$ = n(A) + n( B) $-$ n$\left(\mathrm{A}\cap \mathrm{B}\right)$
$\Rightarrow$110 = 60 + 70 $-$ n$\left(\mathrm{A}\cap \mathrm{B}\right)$
$\Rightarrow$n$\left(\mathrm{A}\cap \mathrm{B}\right)$ = 130 $-$ 110 = 20
∴ There are 20 children who chose both the colours as their favourite.