In an election a voter can vote for two candidates. Half of the voter gave first vote to A & second vote to B, C & D in ratio 1 : 2 : 3. Half of the remaining voters gave their first vote to B & second vote to C & D in ratio 1 : 2. If rest 480 didn’t vote for anyone, find no of votes A got?a)480b)960c)1920d)1440Correct answer is option 'B'. Can you explain this answer?

Question

In an election a voter can vote for two candidates. Half of the voter gave first vote to A & second vote to B, C & D in ratio 1 : 2 : 3. Half of the remaining voters gave their first vote to B & second vote to C & D in ratio 1 : 2. If rest 480 didn&rsquo;t vote for anyone, find no of votes A got?a)480b)960c)1920d)1440Correct answer is option 'B'. Can you explain this answer?

Answer

Given Information:
- Half of the voters gave their first vote to A and second vote to B, C, and D in the ratio 1:2:3.
- Half of the remaining voters gave their first vote to B and second vote to C and D in the ratio 1:2.
- 480 voters did not vote for anyone.

Solution:

Step 1: Total Number of Voters
Let the total number of voters be x.

Step 2: Number of Voters who voted for A and B, C, D
Half of the voters voted for A and B, C, D. So, the number of voters who voted for A and B, C, D is x/2.

Step 3: Number of Voters who voted for A and B, C, D in the ratio 1:2:3
Let the number of voters who voted for A be y. Therefore, the number of voters who voted for B, C, D is 2y and 3y respectively.

So, we have y + 2y + 3y = x/2
=> 6y = x/2
=> y = x/12

Step 4: Number of Voters who voted for B and C, D
Half of the remaining voters voted for B and C, D. So, the number of voters who voted for B and C, D is (x - x/2)/2 = x/4.

Step 5: Number of Votes A got
Since 480 voters did not vote for anyone, the number of voters who voted for A is x - x/2 - x/4 - 480.

Substitute y = x/12 in the above expression:
=> x - x/2 - x/4 - 480 = x - x/12 - 480
=> x - x/2 - x/4 - 480 = 11x/12 - 480
=> x = 480 * 12 = 5760

Therefore, the number of votes A got = 5760 - 5760/2 - 5760/4 - 480 = 960.

Therefore, option B is the correct answer.

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