If A is 50 percent of $B$, then $B$ is what percent of $( A+B) ?$

A. $40$ %

B. $66\frac{2}{3}$ %C. $33\frac{1}{3}$ %D. $75$ %

Given: $A$ is $50$ percent of $B$.
 

To do: To find that $B$ is what percent of $( A+B)$ ?

Solution:

As given, $A$ is $50$ percent of $B$.

$\Rightarrow A=\frac{B}{100}\times 50$

$\Rightarrow A=\frac{B}{2}$

Therefore, $A+B=\frac{B}{2}+B=\frac{3B}{2}$

Let $B$ is $x$ percent of $( A+B)$.

$\Rightarrow B=\frac{3B}{2}\times\frac{x}{100}$

$\Rightarrow 1=\frac{3x}{200}$

$\Rightarrow 3x=200$

$\Rightarrow x=\frac{200}{3}=66\frac{2}{3}$

Therefore, $B$ is $66\frac{2}{3}$ % of $( A+B)$.

Thus, $( B)$ is correct.