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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.
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