In an election between two candidates Joseph and Judith, $60\%$ of the total number of voters did not vote for Joseph and $50\%$ of the total number of voters did not vote for Judith. If it is known that each voter can vote for only one candidate, what percentage of voters did not cast their votes? [With calculator] $\newline$ (A) $5$ $\newline$ (B) $10$ $\newline$ (C) $20$ $\newline$ (D) $30$

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Q. In an election between two candidates Joseph and Judith,

60\%

of the total number of voters did not vote for Joseph and

50\%

of the total number of voters did not vote for Judith. If it is known that each voter can vote for only one candidate, what percentage of voters did not cast their votes? [With calculator]

\newline

(A)

5

\newline

(B)

10

\newline

(C)

20

\newline

(D)

30

Denote Total Voters: Let's denote the total number of voters as $100\%$ for simplicity. According to the problem, $60\%$ of the voters did not vote for Joseph, which means $40\%$ voted for Joseph. Similarly, $50\%$ did not vote for Judith, which implies that $50\%$ voted for Judith. Since each voter can vote for only one candidate, the sum of the percentages of voters for Joseph and Judith should not exceed $100\%$ .
Calculate Combined Votes: Now, let's calculate the percentage of voters who voted for both candidates combined. This is the sum of the percentage of voters for Joseph and the percentage of voters for Judith. However, since no voter can vote for both candidates, this sum should give us the total percentage of voters who actually voted. $\newline$ $40\%$ (voted for Joseph) + $50\%$ (voted for Judith) = $90\%$ (voted in total).
Find Non-Voters: To find the percentage of voters who did not cast their votes, we subtract the percentage of voters who voted from the total number of voters ( $100\%$ ). $\newline$ $100\%$ (total voters) - $90\%$ (voted) = $10\%$ (did not vote).
Percentage of Non-Voters: Therefore, the percentage of voters who did not cast their votes is $10\%$ .