Question

​Anzio, Inc., has two classes of shares. Class B has 10 times the voting rights as Class A. If you own 10 % of the Class A shares and 20 % of the Class B​ shares, what percentage of the total voting rights do you​ hold?

Answer 1

Answer:

$19.1\%$

Step-by-step explanation:

Let x represent voting rights of class A.

We have been given that class B has 10 times the voting rights as Class A. So voting rights of class B would be $10x$.

We have been given that you own 10% of the Class A shares, that will be equal to 10% of x as:

$10\%\text{ of }x=\frac{10}{100}x=0.10x$

We are also told that you own 20% of the Class B​ shares, that will be equal to 20% of $10x$ as:

$20\%\text{ of }10x=\frac{20}{100}\cdot 10x=2x$

Sum of percentage of both class voting rights would be $0.10x+2x=2.10x$.

Total voting rights of both classes would be $x+10x=11x$.

Now we need to find $2.10x$ is what percent of $11x$.

$\text{Percentage of the total voting rights that you hold}=\frac{2.10x}{11x}\times 100\%$

$\text{Percentage of the total voting rights that you hold}=\frac{2.10}{11}\times 100\%$

$\text{Percentage of the total voting rights that you hold}=0.19090909\times 100\%$

$\text{Percentage of the total voting rights that you hold}=19.090909\%$

$\text{Percentage of the total voting rights that you hold}\approx 19.1\%$

Therefore, you hold approximately $19.1\%$ of the total voting rights.