Question

Let $n(A-B)=25+x,$ $n(B-A)=2x$ and $n(A\cap B)=2x$, If $n\left(A\right)=2\left(n\left(B\right)\right)$, then '$x$' is

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is B $5$

$n(A-B)=n\left(A\right)-n(A\cap B)$
$=n\left(A\right)-2x=25+x$
$\Rightarrow n\left(A\right)=25+3x$
$n(B-A)=n\left(B\right)-n(A\cap B)$
$\Rightarrow n\left(B\right)=4x$
$n\left(A\right)=2\left(n\right(B\left)\right)$
$\Rightarrow 25+3x=8x$
$\Rightarrow x=5$